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

If $t$ is a parameter,$A = (a \sec t, b \tan t)$,$B = (-a \tan t, b \sec t)$,and $O = (0, 0)$,then the locus of the centroid of $\triangle OAB$ is:

$A$ rod $PQ$ of length $2a$ moves with its ends on the coordinate axes. Find the locus of the circumcenter of $\Delta OPQ$.

The locus of the centre of a circle passing through $(a, b)$ and cutting orthogonally to the circle $x^2 + y^2 = p^2$ is

$A$ variable circle is described to pass through the point $(1, 0)$ and is tangent to the curve $y = \tan(\tan^{-1} x)$. The locus of the centre of the circle is a parabola whose :

If $P(x, y)$ is a point such that the ratio of the squares of the lengths of the tangents from $P$ to the circles $x^2 + y^2 + 2x - 4y - 20 = 0$ and $x^2 + y^2 - 4x + 2y - 44 = 0$ is $2 : 3$,then the locus of $P$ is a circle with centre