Question

The equation of the circle $C_1$ is $x^2+y^2=4$. The locus of the intersection of orthogonal tangents to the circle is the curve $C_2$ and the locus of the intersection of perpendicular tangents to the curve $C_2$ is the curve $C_3$. Then

• A. $C_3$ is a circle
• B. the area enclosed by the curve $C_3$ is $8\pi$
• C. $C_2$ and $C_3$ are circles with same centre
• D. radius of $C_3$ is twice the radius of $C_2$

Answer 1

Answer: (A), (C)

$C_2$ and $C_3$ are circles with same centre

$C_2$ is director circle of $C_1$.
and $C_2:x^2+y^2=8$
$C_3$ is director circle of $C_2$.
$\therefore C_3:x^2+y^2=16$
So option (a) and (c) are correct