Question

The eccentric angle of a point on the ellipse $\frac{x^{2}}{6} + \frac{y^{2}}{2} = 1$, whose distance from the centre of the ellipse is 2, is

• A. $\pi/4$
• B. $3\pi/2$
• C. $5\pi/3$
• D. $7\pi/6$

Answer 1

Answer: (A)

$\pi/4$

Answer 2

Let $\theta$be the eccentric angle of the point P. Then the coordinates of P are $(\sqrt{6}\cos\theta,\sqrt{2}\sin\theta)$

The centre of the ellipse is at the origin, It is given that $OP = 2$

⇒ $\sqrt{6\cos^{2}\theta + 2\sin^{2}\theta} = 2$⇒ $6\cos^{2}\theta + 2\sin^{2}\theta = 4$⇒

$3\cos^{2}\theta + \sin^{2}\theta = 2$ ⇒ $2\sin^{2}\theta = 1$

⇒ $\sin^{2}\theta = \frac{1}{2}$⇒$\sin\theta = \pm \frac{1}{\sqrt{2}}$⇒ $\theta = \pm \pi/4$