The centres of a set of circles,each of radius $3$,lie on the circle ${x^2} + {y^2} = 25$. The locus of any point in the set is

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

Let $ABCD$ and $AEFG$ be squares of side $4$ and $2$ units,respectively. The point $E$ is on the line segment $AB$ and the point $F$ is on the diagonal $AC$. Then the radius $r$ of the circle passing through the point $F$ and touching the line segments $BC$ and $CD$ satisfies:

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

Let the locus of the point of intersection of the perpendicular tangents drawn to the circle $x^2+y^2+6x-4y-12=0$ be the circle $S$. Then the equation of the tangent drawn to $S$ which is perpendicular to the line $6x-4y+k=0$ is

The locus of a point,such that the difference of the squares of the lengths of the tangents drawn from it to two given circles is constant,is: