The total number of common tangents of $x^{2}+y^{2}-6x-8y+9=0$ and $x^{2}+y^{2}=1$ is

Let $P(a_1, b_1)$ and $Q(a_2, b_2)$ be two distinct points on a circle with center $C(\sqrt{2}, \sqrt{3})$. Let $O$ be the origin and $OC$ be perpendicular to both $CP$ and $CQ$. If the area of the triangle $OCP$ is $\frac{\sqrt{35}}{2}$,then $a_1^2 + a_2^2 + b_1^2 + b_2^2$ is equal to $...........$.

The number of common tangents of the circles $x^2+y^2-4=0$ and $x^2+y^2-6x-8y-24=0$ is

The length of the diameter of the circle which touches the $x-$axis at the point $(1,0)$ and passes through the point $(2,3)$ is:

The equation of the circle which touches the circle $x^2+y^2-6x+6y+17=0$ externally and has the lines $x^2-3xy-3x+9y=0$ as two normals,is

$A$ square is inscribed in the circle $x^2+y^2-2x+4y-93=0$ with its sides parallel to the coordinate axes. Which of the following can be one of the vertices of the square?