If tangents are drawn from point ( 2 + 13cosθ , 3 + 13sinθ ) to ellipse frac{(x-2)^2}{25} + f

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10-2. Parabola, Ellipse, Hyperbola

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If tangents are drawn from the point ($2 + 13cos\theta , 3 + 13sin\theta $) to the ellipse $\frac{(x-2)^2}{25} + \frac{(y-3)^2}{144} = 1,$ then angle between them, is

A

$\frac{\pi }{6}$

B

$\frac{\pi }{3}$

C

$\frac{\pi }{2}$

D

$\frac{2\pi }{3}$

Solution

As the point $(2+13 \cos \theta, 3+13 \sin \theta)$ always lies on the direction circle of the given ellipse

$\frac{(x-2)^{2}}{25}+\frac{(y-3)^{2}}{144}=1,$ so angle between

tangents $=\frac{\pi}{2}$

Standard 11

Mathematics

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