Question

An ellipse is sliding along the coordinate axis. If at a particular instant the foci of the ellipse are at $(1,1)$ and $(3,3),$ then the area of the director circle of the ellipse is

• A. $2\pi$ sq. units
• B. $4\pi$ sq. units
• C. $6\pi$ sq. units
• D. $8\pi$ sq. units

Answer 1

The correct option is D $8\pi$ sq. units

Since $x-$ axis and $y-$axis are perpendicular tangents to the ellipse, so $(0,0)$ lies on the director circle. Also mid point of foci $(2,2)$ is the centre of the circle.

$\therefore$ radius $=\sqrt{2^2+2^2}=2\sqrt{2}$ units

Required area $=\pi (2\sqrt{2}{)}^2=8\pi$ sq. units