Question

Eccentric angle of a point on the ellipse $\frac{x^2}{4}$ + $\frac{y^2}{3}=1$ at a distance $2$ units from the centre of ellipse is:

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $0$

Answer 1

Answer: (C), (D)

$0$
$\pi$

The centre of the ellipse is $(0,0)$

A point on the ellipse is given by $(a\cos \theta ,b\sin \theta )$

So, $a^2{\cos }^2\theta +b^2{\sin }^2\theta =4$

$\Rightarrow 4{\cos }^2\theta +3-3{\cos }^2\theta =4$

$\Rightarrow {\cos }^2\theta =1$

Or $\theta =co{s}^{-1}\left(1\right)$

Thus $\theta =\pi$ or $\theta =0$