Question

Angle between tangents drawn to circle $x^2+y^2=20$, from the point $(6,2)$ is

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $\frac{\pi }{4}$
• D. $2\pi$

Answer 1

The correct option is A $\frac{\pi }{2}$

The equation of tangent to the circle
$x^2+y^2=20$ is $y=mx\pm \sqrt{20}(1+m^2)$.
This tangent passes through the point $(6,2)$
$\therefore {(2-6m)}^2=20(1+m^2)$
$\Rightarrow 2m^2-3m-2=0$
$\Rightarrow m=2,-\frac{1}{2}$
$\therefore$ Required angle $={\tan }^{-1}\left\{\frac{2-\frac{1}{2}}{1+2(-\frac{1}{2})}\right\}$
$={\tan }^{-1}\left(\infty \right)=\frac{\pi }{2}$