The locus of a point which is at a distance of $4$ units from $(3, -2)$ in the $xy$-plane is

From the point $A(0, 3)$ on the circle $x^2 + 4x + (y - 3)^2 = 0$,a chord $AB$ is drawn and extended to a point $M$ such that $AM = 2 AB$. The equation of the locus of $M$ is:

$A$ circle touches the $X$-axis and also touches the circle with radius $2$ and center at $(0, 3)$. Find the locus of the center of the circle.

$A$ chord $AB$ is drawn from the point $A(0,3)$ on the circle $x^2 + 4x + (y - 3)^2 = 0$. If the point $M$ lies on the chord such that $AM = 2AB$,then the locus of point $M$ is:

The locus of the mid-points of the chords of the circle $x^2+y^2=16$ which are tangents to the hyperbola $9x^2-16y^2=144$ is

If a tangent to the circle $x^2 + y^2 = 1$ intersects the coordinate axes at distinct points $P$ and $Q,$ then the locus of the mid-point of $PQ$ is