Question

Locus of the point of intersection of perpendicular tangents to the circle $ x^2 + y^2 = 16 $

• A. $ x^2 + y^2 = 8 $
• B. $ x^2 + y^2 = 32 $
• C. $ x^2 + y^2 = 64 $
• D. $ x^2 + y^2 = 16 $

Answer 1

Answer: (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 $x^{2}+y^{2}=32$