Q. Two perpendicular tangents to the circle $x^{2} + y^{2} = a^{2}$ meet at$P$. Then, the locus of $P$ has the equation
A) $x^{2} + y^{2} = 2a^{2}$
B) $x^{2} + y^{2} = 3a^{2}$
C) $x^{2} + y^{2} = 4a^{2}$
D) None of these
Explanation
(a)
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
Thus, the equation of director circle to the circle $x^{2} + y^{2} = a^{2}$ is $x^{2} + y^{2} = 2a^{2}$
Which is the required locus of point $P$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.