Question

The locus of the point from which mutually perpendicular tangents can be drawn to the circle $x^2+y^2=36$ is

• A. $x^2+y^2=42$
• B. $x^2+y^2=48$
• C. $x^2+y^2=60$
• D. $x^2+y^2=72$

Answer 1

The correct option is D $x^2+y^2=72$

R.E.F image

$x^2+y^2=36$

locus of point from which mutually perpendicular

tangent can be drawn is the

director circle

now we need to find the center and

radius of the director circle

center of director circle =

center of the given circle

= (0,0)

(6,6) is point on

director circle

$\therefore$ radius = $\sqrt{6^2+6^2}=6\sqrt{2}$

$\therefore$ equation of circle $\Rightarrow x^2+y^2=r^2$

$\Rightarrow x^2+y^2=(6\sqrt{2}{)}^2$

$\Rightarrow x^2+y^2=72$