If $A(2, 3)$ and $B(2, -3)$ are two points,then the equation of the locus of a point $P$ such that $PA + PB = 8$ is

At which point on the line $x = 3$ are the tangents drawn to the circle $x^2 + y^2 = 8$ perpendicular to each other?

$A$ variable straight line $AB$ divides the circumference of the circle $x^2 + y^2 = 25$ in the ratio $1 : 2$. If a tangent $CD$ is drawn to the smaller arc parallel to $AB$,such that $ABCD$ is a rectangle,then the locus of $C$ and $D$ is:

The locus of the midpoints of the chords of the circle $x^2-2x+y^2=0$ drawn from the point $(0,0)$ on it is

The angle between a pair of tangents drawn from a point $P$ to the circle ${x^2} + {y^2} + 4x - 6y + 9{\sin ^2}\alpha + 13{\cos ^2}\alpha = 0$ is $2\alpha$. The equation of the locus of the point $P$ is

$A$ circle passes through the point $(3, 4)$ and cuts the circle $x^2 + y^2 = a^2$ orthogonally. The locus of its centre is a straight line. If the distance of this straight line from the origin is $25$,then $a^2$ is equal to: