If a circle $S$ passing through the point $(3,4)$ cuts the circle $x^2+y^2=36$ orthogonally,then the locus of the centre of $S$ is

Let a circle of radius $4$ pass through the origin $O$, the points $A(-\sqrt{3}a, 0)$ and $B(0, -\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab \neq 0$. Then the locus of the centroid of $\Delta OAB$ is a circle of radius

The set of all real values of $\lambda$ for which the point $P$ with coordinates $(\lambda, \lambda^2)$ does not lie inside the triangle formed by the lines $x - y = 0$, $x + y - 2 = 0$, and $x + 3 = 0$ is:

If a circle of constant radius $3k$ passes through the origin $O$ and meets the coordinate axes at $A$ and $B$,then the locus of the centroid of the triangle $OAB$ is

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 locus of the point whose ratio of distance from the origin to its distance from $(-2, -3)$ is $5: 7$,is given by: