The locus of the center of a variable circle which always touches two given circles externally is

If the distance of a variable point $P(x, y)$ from a point $A(2, -2)$ is twice the distance of $P$ from the $Y$-axis,then the equation of the locus of $P$ is:

Let $A = (a, 0)$ and $B = (-a, 0)$ be two fixed points. For $a \in (-\infty, 0)$,point $P(x, y)$ moves in the plane such that $PA = nPB$ $(n \neq 0, n \neq 1)$. If $0 < n < 1$,then which of the following is true regarding the locus of $P$?

The number of solid cones with integer radius and integer height each having its volume numerically equal to its total surface area is

The locus of the point of intersection of perpendicular tangents to the circle $x^{2}+y^{2}=16$ is

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