Question

The locus of the point of intersection of tangents to the circle $x=a\cos \theta ,y=a\sin \theta$ at the points, whose parametric angles differ by $\frac{\pi }{2}$ is

• A. a straight line
• B. a circle
• C. a pair of straight lines
• D. None of these

Answer 1

The correct option is B a circle

$x=a\cos \theta ,y=a\sin \theta$
$\Rightarrow S:x^2+y^2=a^2$
Let from point $P,$ tangents are drawn.

$\because \angle AOB=\frac{\pi }{2},$
$\therefore \angle APB=\frac{\pi }{2}$
So, tangents are perpendicular to each other.
Hence $P$ will lie on director circle of $S$ which is also a circle.