Question

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

(a) 0

(b) $\frac{\pi}{3}$

(c) $\frac{\pi}{6}$

(d) $\frac{\pi}{2}$

Answer 1

Let equation of line passing, through $(0,0)$ be $y-m x=0$ and it is a tangent to the circle $(x-7)^2+(y+1)^2=25$, if

$\frac{-1-7 m}{\sqrt{1+m^2}}=5 \Rightarrow m=\frac{3}{4},-\frac{4}{3}$

Now, $\frac{3}{4} \times\left(-\frac{4}{3}\right)=-1$

Hence, angle between tangents is $\frac{\pi}{2}$

So, The correct option of this question will be (D).