$A(2,3)$ and $B(-1,1)$ are two points. If $P(x,y)$ is a variable point such that $\angle APB = 90^{\circ}$,then the locus of $P$ is:

Find the equation of the circle with center $(3, 1)$ and touching the line $8x - 15y + 25 = 0$.

If $x = 2 + 3 \cos \theta$ and $y = 1 - 3 \sin \theta$ represent a circle,then the centre and radius are:

The equation of the circle touching the lines $|x-2|+|y-3|=4$ is

The equation $ax^2 + 2y^2 + 2bxy + 2x - y + c = 0$ represents a circle passing through the origin,if:

If three distinct points $A, B, C$ are given in the $2$-dimensional coordinate plane such that the ratio of the distance from $(1, 0)$ to the distance from $(-1, 0)$ is equal to $\frac{1}{2}$,then the circumcentre of the triangle $ABC$ is at the point