The centre of an ellipse is C and PN is any o | vedclass

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Question

(a) Let ellipse be $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

$P = (a\cos 	heta ,\,b\sin 	heta ),\,A\,{m{ and}}\,A' \equiv ( \

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$\frac{{{b^2}}}{{{a^2}}}$

Vedclass · Answer

(a) Let ellipse be $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

$P = (a\cos 	heta ,\,b\sin 	heta ),\,A\,{m{ and}}\,A' \equiv ( \pm a,0),\,\,$

$N \equiv (a\cos 	heta ,0),$

$PN = b\sin 	heta ,$$AN = a(1 - \cos 	heta ),$

$A'N = a(1 + \cos 	heta )$

$\frac{{{{(PN)}^2}}}{{AN\,A'N}} = \frac{{{b^2}{{\sin }^2}	heta }}{{{a^2}(1 - \cos 	heta )(1 + \cos 	heta )}} = \frac{{{b^2}}}{{{a^2}}}$.

The centre of an ellipse is $C$ and $PN$ is any ordinate and $A$, $A’$ are the end points of major axis, then the value of $\frac{{P{N^2}}}{{AN\;.\;A'N}}$ is

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