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		<title>Sticky Note!</title>
		<link>http://ginryuukurochan.wordpress.com/2008/09/28/sticky-note/</link>
		<comments>http://ginryuukurochan.wordpress.com/2008/09/28/sticky-note/#comments</comments>
		<pubDate>Sun, 28 Sep 2008 05:15:46 +0000</pubDate>
		<dc:creator>Jade Phoenix</dc:creator>
				<category><![CDATA[Uncategorized]]></category>
		<category><![CDATA[important]]></category>
		<category><![CDATA[note]]></category>

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		<description><![CDATA[Due to loads of distractions ( which includes my laziness ), I haven&#8217;t been able to keep up with updating this blog in the last few months. This note is just to say that I won&#8217;t be able to continue blogging here for at least a few months more. After that, all that gets updated [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=ginryuukurochan.wordpress.com&amp;blog=1796611&amp;post=13&amp;subd=ginryuukurochan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Due to loads of distractions ( which includes my laziness ), I haven&#8217;t been able to keep up with updating this blog in the last few months. This note is just to say that I won&#8217;t be able to continue blogging here for at least a few months more. After that, all that gets updated here would be more of my personal notes or kind from whatever I study, which will not be limited to Maths and Physics, and which will completely exclude Chemistry. Though I might post some topics from it randomly as it is something I really love to study.</p>
<p>Anyway, thanks for all your comments! When I&#8217;d started this blog initially, I only thought of it as a place to gather my notes. Never really thought that it might actually help someone out. (-: Glad to know that!</p>
<p>So then, till next time!~</p>
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		<title>Nomenclature of Organic Compounds</title>
		<link>http://ginryuukurochan.wordpress.com/2007/09/30/nomenclature-of-organic-compounds/</link>
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		<pubDate>Sun, 30 Sep 2007 05:14:01 +0000</pubDate>
		<dc:creator>Jade Phoenix</dc:creator>
				<category><![CDATA[Organic chemistry]]></category>
		<category><![CDATA[basic concepts]]></category>
		<category><![CDATA[functional groups]]></category>
		<category><![CDATA[IUPAC]]></category>
		<category><![CDATA[nomenclature]]></category>
		<category><![CDATA[rules]]></category>

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		<description><![CDATA[Rules ( according to IUPAC ) : 1. Count the total number of carbon atoms. 2. Number them from an end. If other groups are present, number them according to the following priority ( decreasing ) list : -COOH , -COCl , ( R – alkyl group ) , -CONH2 , -CN , -HC=O , [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=ginryuukurochan.wordpress.com&amp;blog=1796611&amp;post=12&amp;subd=ginryuukurochan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p class="MsoNormal"><u><span style="font-size:10pt;font-family:Arial;">Rules</span></u><span style="font-size:10pt;font-family:Arial;"> ( according to IUPAC ) :</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">1. Count the <strong>total</strong> number of carbon atoms.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">2. Number them from an end. If other groups are present, number them according to the following <strong>priority ( decreasing )</strong> list :</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">-COOH , -COCl , ( R – alkyl group ) , -CONH<sub>2</sub> , -CN , -HC=O , &gt;C=O , -OH , -NH<sub>2</sub> , &gt;C=C&lt; , -C<s>=</s>C- </span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">R , C<sub>6</sub>H<sub>5</sub>- , OR , Cl , Br , NO<sub>2</sub> etc. are prefix substituents.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">3. If <strong>more than one</strong> functional group are present, they are numbered by adding di, tri etc before the class suffix.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">4. All the names should have the names of individual groups arranged in <strong>alphabetical order</strong>.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">5. In the name, <strong>two vowels</strong> ( one at the end of one group and other at start of another ) <strong>should</strong> <strong>never come together</strong>. The last letter of the prefix group should be changed to a consonantand only if this is not possible should the first letter of the suffix group be changed.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">6. The <strong>carbon number</strong> to which <strong>any group is attached</strong> should be <strong>written right before it</strong>, and not at the beginning of the name.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">7. In case of <strong>branched chains</strong>, they are <strong>named as</strong> <strong>alkyl groups</strong>, separately <strong>as a chain</strong>, and their names are <strong>enclosed in brackets</strong>.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">8. The substituents are given the lowest numbers possible, so that in the final name, the total of numbers is the lowest possible for the compound. But, of course, the priority list is followed.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">9. Numerical prefixes <strong>‘ bis ‘, ‘ tris ‘</strong> etc., are used to indicate <strong>multiplicity of substituted</strong> <strong>substituent</strong>.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"></span></p>
<p class="MsoNormal">&nbsp;</p>
<p class="MsoNormal"><img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/Biscompound.gif" alt="Bis" height="191" width="245" /></p>
<p class="MsoNormal">&nbsp;</p>
<p class="MsoNormal"><u><span style="font-size:10pt;font-family:Arial;">Functional Groups</span></u><span style="font-size:10pt;font-family:Arial;"> : ( all of the above rules have to applied )</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">1. Alkane : -ane [ methane, propane, heptane ]</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Trivial naming :</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/secbutyl.gif" alt="sec butyl" height="79" width="109" />                             <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/isobutyl.gif" alt="isobutyl" />          </span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/tertbutyl.gif" alt="tertbutyl" height="107" width="86" />                            <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/neopentyl.gif" alt="neopentyl" /></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"> </span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">2. Alkene : -ene [methene, propene, heptene ]</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">3. Alkyne : -yne [methyne, propyne, heptyne ]</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">4. Alcohol : -ol , hydroxy-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Acc. to new rules, if more than two alcohol groups are attached in succession to a chain of carbon atoms, the naming is done as, for example, propane &#8211; 1, 2 , 3 – carbol.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">CH<sub>2</sub> – CH – CH<sub>2</sub></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><span>   </span>|<span>                  </span>|<span>        </span>|</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">OH<span>    </span>OH<span>       </span>OH</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">5. Aldehyde : -al , oxo- , formyl-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Acc. to new rules, if more than two aldehyde groups are attached in succession to a chain of carbon atoms, the naming is done as, for example, propane &#8211; 1, 2 , 3 – carbaldehyde.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">CH<sub>2</sub> – CH – CH<sub>2</sub></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><span>   </span>|<span>                  </span>|<span>               </span>|</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">CHO<span>   </span>CHO<span>   </span>CHO</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">6. Ketone : -one , oxo-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">7. Ether : alkoxy alkane ( R-O-R’ )</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Aliphatic – R = chain having less carbon atoms</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Aromatic – R = the aliphatic chain attached to a benzene ring</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Aromatic – If another aromatic group is present instead of an aliphatic chain, the compound is named using di, tri etc.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">8. Nitrile : -nitrile* ( the last letter ‘e’ of the primary suffix is not removed ) , cyano-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">9. Isocyanide : alkyl isocyanide , alkyl isonitrile , alkyl carbylamine</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">10. Amine : -amine , amino-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">11. Acid : -oic acid</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">12. Ester : alkyl alkanoate – alkyl = alocohol part , alkanoate = acid part</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">13. Halide : halo-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">14. Amide : -amide , carbamoyl-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">15. Nitro : nitro-</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">16. Acid Halide : -oyl halide</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">17. <strong>Aromatic Compounds</strong> <strong>: </strong>These are more commonly known by their trivial names. They follow all the above listed rules as such. A special rule of aromatics is the definitions of ortho, meta and para substitutions, and naming based on it.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">18. <strong>Cyclo Compounds :</strong> These are named exactly as the aliphatic compounds, just with a ‘ cyclo ’ added before the primary ring suffix. Another important rule is that if a side chain attached to the ring contains a multiple bond or a functional group, the alicylic ring is treated as substituent irrespective of the size of the ring.</span></p>
<p><span style="font-size:10pt;font-family:Arial;"></span></p>
<p class="MsoNormal"> <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/cyclo1.gif" alt="cyclo 1" />                             <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/cyclo2.gif" alt="cyclo 2" /></p>
<p class="MsoNormal">&nbsp;</p>
<p class="MsoNormal"><u><span style="font-size:10pt;font-family:Arial;"><span style="text-decoration:none;"></span></span></u></p>
<p><span style="font-size:10pt;font-family:Arial;"></span></p>
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		<title>Basic Concepts of Organic Chemistry</title>
		<link>http://ginryuukurochan.wordpress.com/2007/09/28/basic-concepts-of-organic-chemistry/</link>
		<comments>http://ginryuukurochan.wordpress.com/2007/09/28/basic-concepts-of-organic-chemistry/#comments</comments>
		<pubDate>Fri, 28 Sep 2007 16:37:43 +0000</pubDate>
		<dc:creator>Jade Phoenix</dc:creator>
				<category><![CDATA[Organic chemistry]]></category>
		<category><![CDATA[basic concepts]]></category>
		<category><![CDATA[basic hybridisation]]></category>
		<category><![CDATA[projection formulae]]></category>
		<category><![CDATA[structural formulae]]></category>

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		<description><![CDATA[General Organic Chemistry Basic Concepts 1. Property of catenation &#8211; leads to a variety of covalent compounds. 2. First organic compound prepared in lab &#8211; by Wohler &#8211; Urea from ammonium cyanate. NH4CNO &#8211;&#62; NH2CONH2 3. First organic compound synthesised from its elements – by Kolbe – Acetic acid. 4. Hybridisation : sp3 , sp2 [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=ginryuukurochan.wordpress.com&amp;blog=1796611&amp;post=11&amp;subd=ginryuukurochan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p class="MsoNormal"><strong><u><span style="font-size:10pt;font-family:Arial;">General Organic Chemistry</span></u></strong><span style="font-size:10pt;font-family:Arial;"></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"> </span><u><span style="font-size:10pt;font-family:Arial;">Basic Concepts</span></u><span style="font-size:10pt;font-family:Arial;"></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"> 1. Property of <strong>catenation</strong> &#8211; leads to a variety of covalent compounds.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"> 2. First organic compound prepared in lab &#8211; by Wohler &#8211; Urea from ammonium cyanate.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">NH<sub>4</sub>CNO <span> </span>&#8211;&gt; <span> </span>NH<sub>2</sub>CONH<sub>2</sub></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"> 3. First organic compound synthesised from its elements – by Kolbe – Acetic acid.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"> 4. <strong>Hybridisation</strong> <strong>:</strong> sp<sup>3</sup> , sp<sup>2</sup> , sp – influences the bond length, bond enthalpy and electronegativity of org compounds.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Bond length – sp<sup>3</sup> &gt; sp<sup>2</sup> &gt; sp</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Bond enthalpy – sp<sup>3</sup> &lt; sp<sup>2</sup> &lt; sp</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">Electronegativity ( depends on % of s character ) – sp<sup>3</sup> &lt; sp<sup>2</sup> &lt; sp</span></p>
<p class="MsoNormal"><img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/ethane.gif" alt="sp3" height="99" width="89" />             <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/ethene.gif" alt="sp2" height="81" width="63" />              <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/ethyne.gif" alt="sp" height="37" width="55" /></p>
<p class="MsoNormal">&nbsp;</p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">5. <strong>Structural Representations :</strong> Lewis structures, complete, condensed and bond-line structural formulae.</span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><strong>Complete</strong> Structural Formula : </span></p>
<p class="MsoNormal"><img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/ethane-complete.gif" />             <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/ethene-complete.gif" />             <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/ethyne-complete.gif" /></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><strong>Condensed</strong> Structural Formula : </span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">CH<sub>3</sub>CH<sub>3</sub> , CH<sub>3</sub>OH , H<sub>2</sub>C=CH<sub>2</sub></span></p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;"><strong>Bond-line</strong> Structural Formula : </span></p>
<p><img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/Bond-line.gif" />                      <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/Bond-line2.gif" /></p>
<p class="MsoNormal">&nbsp;</p>
<p class="MsoNormal"><span style="font-size:10pt;font-family:Arial;">6. 3D Representation on paper : Solid and dashed wedges are used to represent a 3D structure. Normally known as <strong>wedge-and-dash</strong> structure, wedges are used to indicate atom/molecule jutting out of paper, and dashes for atom/molecule going in.</span></p>
<p>    <span style="font-size:10pt;font-family:Arial;">7. <strong>Projection Formulae :</strong> Molecules are observed in a ray of light, and using some conventions, are presented in a 2D form on paper. Different projection formulae include – Fischer projection, Newman projection, and Sawhorse projection formulae.</span></p>
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			<media:title type="html">Jade Phoenix</media:title>
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		<title>Parabola</title>
		<link>http://ginryuukurochan.wordpress.com/2007/09/26/parabola/</link>
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		<pubDate>Wed, 26 Sep 2007 21:08:45 +0000</pubDate>
		<dc:creator>Jade Phoenix</dc:creator>
				<category><![CDATA[Co-ordinate Geometry - 2D]]></category>
		<category><![CDATA[chord]]></category>
		<category><![CDATA[conics]]></category>
		<category><![CDATA[directrix]]></category>
		<category><![CDATA[double ordinate]]></category>
		<category><![CDATA[eccentricity]]></category>
		<category><![CDATA[focal chord]]></category>
		<category><![CDATA[focus]]></category>
		<category><![CDATA[latus rectum]]></category>
		<category><![CDATA[parabola]]></category>
		<category><![CDATA[vertex]]></category>

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		<description><![CDATA[Conic Sections A conic section is the locus of a point which moves so that its distance from a fixed point ( focus ) is in a constant ratio ( eccentricity ) with a fixed straight line ( directrix ). Eccentricities : e = 1 - Parabola e &#60; 1 - Ellipse e &#62; 1 [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=ginryuukurochan.wordpress.com&amp;blog=1796611&amp;post=6&amp;subd=ginryuukurochan&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Conic Sections</span></strong></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">A conic section is the locus of a point which moves so that its distance from a fixed point ( <strong>focus</strong> ) is in a constant ratio ( <strong>eccentricity</strong> ) with a fixed straight line ( <strong>directrix</strong> ).</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Eccentricities :</span></strong></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">e = 1<span>  </span>-<span>  </span>Parabola</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">e &lt; 1<span>  </span>-<span>  </span>Ellipse</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">e &gt; 1<span>  </span>-<span>  </span>Hyperbola</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">e = sqrt. 2<span>  </span>-<span>  </span>Rectangular Hyperbola</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span><span id="more-6"></span><strong><u><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Parabola :</span></u></strong></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"> <img src="http://i206.photobucket.com/albums/bb239/ginryuu_kurochan/Parabola.jpg" alt="Parabola" align="absmiddle" height="335" width="258" /></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">&nbsp;</p>
<p align="justify"><!--[if !supportLists]--><span style="font-size:10pt;font-family:Symbol;"><span></span></span></p>
<ul>
<li><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Standard form :</span></strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> y<sup>2</sup> = 4ax</span></li>
</ul>
<p align="justify"><!--[if !supportLists]--></p>
<ul>
<li><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Dist. FV = Dist. VD ( where F = focus, V = vertex, D = point on directrix and axis; and F, V, D are collinear )</span></li>
</ul>
<p align="justify"><!--[endif]--><!--[if !supportLists]--><span style="font-size:10pt;font-family:Symbol;"> </span></p>
<ul>
<li><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Terms : Chord, Focal chord, Double ordinate ( _|_ chord ), Latus rectum ( double ordinate through focus )</span></li>
</ul>
<p align="justify"><!--[if !supportLists]--><span style="font-size:10pt;font-family:Symbol;"> </span><!--[endif]--></p>
<ul>
<li><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Latus Rectum : Length = 4a</span><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">        Eq. – x = a ( for the standard form )</span></li>
</ul>
<ul>
<li><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">General Eq. :</span></strong></li>
</ul>
<p align="justify"><!--[if !supportLists]--><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span>          </span>    ( h , k ) </span><span style="font-size:10pt;font-family:Wingdings;"><span>&#8211;&gt;</span></span><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> focus</span><br />
<span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span>          </span>    ( x , y ) </span><span style="font-size:10pt;font-family:Wingdings;"><span>&#8211;&gt;</span></span><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> any pt. on the parabola</span><br />
<span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span>          </span>    ax + by + c = 0 </span><span style="font-size:10pt;font-family:Wingdings;"><span>&#8211;&gt;</span></span><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> directrix</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    sqrt. [ ( x – h )<sup>2</sup><span>  </span>+<span>  </span>( y – k )<sup>2</sup> ] = ( ax + by + c ) / ( sqrt. ( a<sup>2</sup> + b<sup>2</sup> ) )</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    Solving which, we arrive at –</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    ( b<sup>2</sup>x<sup>2</sup> + a<sup>2</sup>y<sup>2</sup> – 2abxy ) + xterm + yterm + constant = 0<br />
</span></p>
<p class="MsoNormal" style="text-indent:-46.5pt;margin:0 -1.25in 0.0001pt 73.5pt;" align="justify"><!--[if !supportLists]--><span style="font-size:10pt;font-family:Wingdings;"><span><strong>=&gt;  </strong></span></span><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">( bx – ay )<sup>2</sup> + 2gx + 2fy + d = 0</span></strong></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"> <span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span></span><strong>The second degree terms form a perfect square. This is a characteristic property of a parabola.</strong></span></p>
<ul>
<li>  <span style="font-size:10pt;font-family:Symbol;"> <span><span style="font-family:'Times New Roman';font-style:normal;font-variant:normal;font-weight:normal;font-size:7pt;line-height:normal;"></span></span></span><!--[endif]--><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Helpful notes for solving problems :</span></li>
</ul>
<ol>
<li><!--[if !supportLists]--><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span><span style="font-family:'Times New Roman';font-style:normal;font-variant:normal;font-weight:normal;font-size:7pt;line-height:normal;">      </span></span></span><!--[endif]--><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Express the given equation in its standard form shifting the origin.</span></li>
<li> <!--[if !supportLists]--><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span><span style="font-family:'Times New Roman';font-style:normal;font-variant:normal;font-weight:normal;font-size:7pt;line-height:normal;">      </span></span></span><!--[endif]--><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Make the terms of the second degree a perfect square. It’s usually convenient to divide by the coefficient of the x-2<sup>nd</sup> degree-term.</span></li>
</ol>
<ul>
<li> <span style="font-size:10pt;font-family:Symbol;"><span><span style="font-family:'Times New Roman';font-style:normal;font-variant:normal;font-weight:normal;font-size:7pt;line-height:normal;"></span></span></span><!--[endif]--><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Parametric Equations : </span></strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">y<sup>2</sup> = 4ax</span></li>
</ul>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span>      </span>    =&gt;<span>    </span><strong>( y / 2a ) = ( 2x / y ) = t – Basic equation</strong></span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    =&gt;<span>    </span><strong>x = at<sup>2</sup><span>  </span>,<span>  </span>y = 2at</strong> – where ‘ t ’<span>  </span>is the parameter.</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span></span>Tangent :<br />
Eq. of the chord joining points ( at<sub>1</sub><sup>2</sup> , 2at<sub>1</sub> ) and ( at<sub>2</sub><sup>2</sup> , 2at<sub>2</sub> ) can be found, and the second point can be replaced by the former to obtain the tangent.</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"> <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Normal</span><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> :</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">The slope obtained from the tangent equation can be m<sub>1</sub>.</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"> <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">m<sub>1</sub>m<sub>2</sub> = -1 ( for perpendicular lines )</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"> <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Therefore, slope for normal ( m<sub>2</sub> ) = ( -1 / m<sub>1</sub> ).</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Parametric Eq. for tangent &amp; normal :</span></strong></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">T =&gt;<span>  </span>yt = x + at<sup>2</sup> ( t = t1, from above )</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">N =&gt;<span>  </span>y – 2at = -xt + at<sup>3</sup> ( t = t1, from above )</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">General Eq. for tangent &amp; normal :</span></strong><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> This is obtained by substituting x<sub>1</sub> = at<sup>2</sup> and y<sub>1</sub> = 2at in the above equations, where P( x<sub>1</sub> , y<sub>1</sub> ) lies on the parabola.</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">T =&gt;<span>  </span>yy<sub>1</sub> = 2a ( x + x<sub>1</sub> )</span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify">&nbsp;</p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">N =&gt;<span>  </span>2ay – 2ay<sub>1</sub> = -xy<sub>1</sub> + x<sub>1</sub>y<sub>1</sub></span></p>
<p class="MsoNormal" style="margin:0 -1.25in 0.0001pt 27pt;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
<ul>
<li> <!--[if !supportLists]--><span style="font-size:10pt;font-family:Symbol;"><span></span></span><span style="font-size:10pt;font-family:'MS Reference Sans Serif';">Co – ordinates of focal chord :</span></li>
</ul>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"><span>       </span><strong>    P ( at<sub>1</sub><sup>2</sup> , 2at<sub>1</sub> )</strong> , Q ( at<sub>2</sub><sup>2</sup> , 2at<sub>2</sub> ) &amp; F ( a, 0 )</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    Slope PF = Slope PQ</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    ( 2at<sub>1</sub> – 0 ) / ( at<sub>1</sub><sup>2</sup> – a ) = ( 2at<sub>1</sub> – 2at<sub>2</sub> ) / ( at<sub>1</sub><sup>2</sup> – at<sub>2</sub><sup>2</sup> )</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    =&gt;<span>    </span>t<sub>1</sub> / ( t<sub>1</sub><sup>2</sup> -1 ) = 1 / ( t<sub>1</sub> + t<sub>2</sub> )</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    =&gt;<span>    </span>t<sub>1</sub><sup>2</sup> + t<sub>1</sub>t<sub>2</sub> = t<sub>1</sub><sup>2</sup> &#8211; 1</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    =&gt;<span>    </span>t<sub>2</sub> = -1 / t<sub>1</sub></span></p>
<p class="MsoNormal" style="margin-right:-1.25in;" align="justify">     <span style="font-size:10pt;font-family:'MS Reference Sans Serif';">    Hence, <strong>Q ( a/t<sub>1</sub><sup>2</sup> , -2a/t<sub>1</sub> )</strong> is the other co-ordinate.</span></p>
<p class="MsoNormal" style="margin-right:-1.25in;"><span style="font-size:10pt;font-family:'MS Reference Sans Serif';"> </span></p>
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