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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