The locus of the centre of the circle,which cuts the circle $x^2+y^2-20x+4=0$ orthogonally and touches the line $x=2$,is

The set of all points that are at a distance of at least $2$ units from $(-3, 0)$ is

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 $\pi / 2$ is:

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

If the angle between a pair of tangents drawn from a point $P$ to the circle $x^2+y^2-4x+2y+3=0$ is $\frac{\pi}{2}$,then the locus of $P$ is

Two perpendicular tangents to the circle $x^2 + y^2 = a^2$ meet at point $P$. The equation of the locus of $P$ is: