Question

The locus of the perpendicular tangents to the circle whose parametric equation is $x=a\cos \theta ,y=a\sin \theta$ is given by

• A. equation of director circle of $x^2+y^2=2a^2$
• B. equation of director circle of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
• C. $x^2+y^2=4a^2$
• D. $x^2+y^2=\frac{a^2}{4}$

Answer 1

Answer: (A)

equation of director circle of $x^2+y^2=2a^2$

Cartesian form of circle is $x^2+y^2=a^2$
The locus of point of intersection of perpendicular tangents to the circle $x^2+y^2=a^2$ is a director circle which is $x^2+y^2=2a^2$
Ans: A