If tangents are drawn from point P(3 sinθ + 4 cosθ , 3 cosθ - 4 sinθ) , θ = frac {π}{8}

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10-2. Parabola, Ellipse, Hyperbola

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If tangents are drawn from point $P(3\ sin\theta + 4\ cos\theta , 3\ cos\theta\ -\ 4\ sin\theta)$ , $\theta = \frac {\pi}{8}$ to the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$ then angle between the tangents is

A

$\frac {\pi}{8}$

B

$\frac {\pi}{4}$

C

$\frac {3\pi}{8}$

D

$\frac {\pi}{2}$

Solution

Point $P$ lie on director circle of given ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$

$\therefore $ angle between tangents is $\frac {\pi}{2}$

Standard 11

Mathematics

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