Question

$The$ ordinates of 4 points on the ellipse $\frac{x^2}{16}+\frac{y^2}{4}=1$ are $\sqrt{2},\sqrt{3},1,2$. The eccentric angles cooresponding to the points arranged in the increasing order are:

(Take $A:\sqrt{2},B:\sqrt{3},C$: 1, $D$ :2)

• A. D,B,A,C
• B. C,A,B,D
• C. A,B,C,D
• D. C,D,A,B

Answer 1

The correct option is B C,A,B,D

The eccentric angle $\theta$ corresponding to point $y$ is given by

$b\sin \theta =y$

$\left(1\right)2\sin \theta =\sqrt{2}$

$⟹\sin \theta =\frac{1}{\sqrt{2}}$

$⟹\theta ={45}^0$

$\left(2\right)2\sin \theta =\sqrt{3}$

$⟹\sin \theta =\frac{\sqrt{3}}{2}$

$⟹\theta ={60}^0$

$\left(3\right)2\sin \theta =1$

$⟹\sin \theta =\frac{1}{2}$

$⟹\theta ={30}^0$

$\left(4\right)2\sin \theta =2$

$⟹\sin \theta =1$

$⟹\theta ={90}^o$

Then angles corresponding to the points in increasing order are given by

$C,A,B,D$