If $A(5, -4)$ and $B(7, 6)$ are points in a plane, then the set of all points $P(x, y)$ in the plane such that $AP:PB = 2:3$ is

The locus of a point $P(x, y)$ satisfying the equation $\sqrt{(x-2)^2+y^2}+\sqrt{(x+2)^2+y^2}=4$ is:

The equation of the image of the circle $x^2 + y^2 + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ 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 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 mid-points of the chords of the circle $x^{2}+y^{2}+2x-2y-2=0$ which make an angle of $90^{\circ}$ at the centre is