Question

Locus of the point of intersection of the pair of perpendicular tangents to the circles $x^2+y^2=1$ and $x^2+y^2=7$ is the director circle of the circle with radius.

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

Answer 1

The correct option is C $2\sqrt{2}$

We know that,

It's a circle with center $O$ ,

So, we need a point to find the radius.

$x=\sqrt{7}$,the intersection $(1,\sqrt{7})$ is on the circle

The radius is

$\begin{array}{c}=\sqrt{1^2+{\sqrt{7}}^2}\\ =\sqrt{8}\\ =2\sqrt{2}\end{array}$