Eccentric angle of a point on ellipse {x^2} + 3{y^2} = 6 at a distance 2 units from centre of ellips

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10-2. Parabola, Ellipse, Hyperbola

hard

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

A

$\frac{\pi }{4}$

B

$\frac{\pi }{3}$

C

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

D

$(a)$ and $(c)$ both

Solution

(d) Let the eccentric angle of the point be $\theta $, then its co-ordinates are $(\sqrt 6 \cos \theta ,\sqrt 2 \sin \theta ).$

Hence $6{\cos ^2}\theta + 2{\sin ^2}\theta = 4$ or ${\cos ^2}\theta = \frac{1}{2}$

Hence, $\cos \theta = \pm \frac{1}{{\sqrt 2 }}$,

$\theta = \frac{\pi }{4}$or $\frac{{3\pi }}{4}$.

Standard 11

Mathematics

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