Question

Eccentric angle of a point on the ellipse $x^2+3y^2=6$ at a distance $\sqrt{3}$ units from the centre of the ellipse is

• A. $\frac{5\pi }{3}$
• B. $\frac{\pi }{3}$
• C. $\frac{3\pi }{4}$
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (C)

$\frac{3\pi }{4}$

$Letthepointsbe(\sqrt{3}cos\theta ,\sqrt{3}sin\theta )and(-\sqrt{3}cos\theta ,-\sqrt{3}sin\theta )Thispointsliesontheellipse{x}^2+3y^2=6Then,3{\left(cos\theta \right)}^2+9{\left(sin\theta \right)}^2=6Or,6{\left(sin\theta \right)}^2=3Or,sin\theta =\frac{\pm 1}{\sqrt{2}}\therefore \theta =\frac{\Pi }{4},\frac{3\Pi }{4}$

Option [C] is the answer