If the circles $x^2+y^2+2 \alpha x+2 y-8=0$ and $x^2+y^2-2 x+a y-14=0$ intersect orthogonally, then the distance between their centres is

If the axes are rotated through angle ' $\alpha$ ', then the number of values of a such that the transformed equation of $x^2+y^2+2 x+2 y-5=0$ contains no liner terms is

The triangle $P Q R$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$, then $\angle Q P R$ is equal to

The locus of the point of intersection of perpendicular tangents drawn to the circle $x^2+y^2=10$ is