The locus of the centers of the circles which cut the circles $x^2 + y^2 + 4x - 6y + 9 = 0$ and $x^2 + y^2 - 5x + 4y - 2 = 0$ orthogonally is

The locus of the centre of a circle which passes through the origin and cuts off a length of $4$ units from the line $x=3$ is

If the locus of the midpoints of the chords of the circle $x^2+y^2=25$,which subtend a right angle at the origin,is given by $\frac{x^2}{a^2}+\frac{y^2}{a^2}=1$,then $|a|=$

$A$ 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:

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 centres of all circles which touch the line $x=2a$ and cut the circle $x^2+y^2=a^2$ orthogonally is: