The eccentric angles of the extremities of la | vedclass

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Question

(c) Coordinates of any point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

whose eccentric angle is $	heta $ are $(a\cos

Vedclass · Accepted Answer

${	an ^{ - 1}}\left( { \pm \frac{b}{{ae}}} ight)$

Vedclass · Answer

(c) Coordinates of any point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$

whose eccentric angle is $	heta $ are $(a\cos 	heta ,\,\,b\sin 	heta ).$

The coordinates of the end points of latus recta are $\left( {ae,\, \pm \frac{{{b^2}}}{a}} ight).$

$	herefore a\cos 	heta = ae$ and $b\sin 	heta = \pm \frac{{{b^2}}}{a}$

$&rArr; 	an 	heta = \pm \frac{b}{{ae}} $

$\Rightarrow 	heta = {	an ^{ - 1}}\left( { \pm \frac{b}{{ae}}} ight)$.

The eccentric angles of the extremities of latus recta of the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ are given by

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