Q. Locus of the point of intersection of perpendicular tangents to the circle $x^{2} + y^{2} = 16$ is
A) $x^{2} + y^{2} = 8$
B) $x^{2} + y^{2} = 32$
C) $x^{2} + y^{2} = 64$
D) $x^{2} + y^{2} = 16$
Explanation
(b)
We know that, if two perpendicular tangents to the circle $x^{2} + y^{2} = a^{2}$ meet at $P$, then the point $P$ lies on a director circle
$\therefore$ Required locus is $x^{2} + y^{2} = 32$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.