Angle between tangents drawn from the origin to circle (x -7)^2 + (y + 1)^2 = 25 is :-

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10-1.Circle and System of Circles

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The angle between the tangents drawn from the origin to the circle $(x -7)^2 + (y + 1)^2 = 25$ is :-

A

$\frac{\pi}{3}$

B

$\frac{\pi}{6}$

C

$\frac{\pi}{2}$

D

$\frac{\pi}{8}$

Solution

Let the equation of tangent drawn from (0,0) to the circle be $y=m x$. Then, $p=a \Rightarrow \frac{7 m+1}{\sqrt{m^{2}+1}}=5$

$\Rightarrow 24 m^{2}+14 m-24=0$

$\Rightarrow 12 m^{2}+7 m-12=0$

$\Rightarrow m_{1} m_{2}=\frac{-12}{12}=-1$

$\because$ Required angle $=\frac{\pi}{2}$

Standard 11

Mathematics

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