The eccentric angles of the extremities of th | vedclass

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(C) The coordinates of any point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with eccentric angle $	heta$ are $(a \cos 	heta, b \sin 	he

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

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(C) The coordinates of any point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with eccentric angle $	heta$ are $(a \cos 	heta, b \sin 	heta)$.The coordinates of the endpoints of the latus recta are $(ae, \pm \frac{b^2}{a})$.Equating the coordinates,we have $a \cos 	heta = ae$ and $b \sin 	heta = \pm \frac{b^2}{a}$.From $a \cos 	heta = ae$,we get $\cos 	heta = e$.From $b \sin 	heta = \pm \frac{b^2}{a}$,we get $\sin 	heta = \pm \frac{b}{a}$.Therefore,$	an 	heta = \frac{\sin 	heta}{\cos 	heta} = \frac{\pm b/a}{e} = \pm \frac{b}{ae}$.Thus,$	heta = 	an^{-1}\left( \pm \frac{b}{ae} ight)$.

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

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