The circles $x^2 + y^2 = 9$ and $x^2 + y^2 - 12y + 27 = 0$ touch each other. The equation of their common tangent is

The equation of the chord of contact,if the tangents are drawn from the point $(5, -3)$ to the circle $x^2 + y^2 = 10$,is

The area of the triangle formed by the tangents from the point $(h, k)$ to the circle $x^2 + y^2 = a^2$ and the line joining their points of contact is

$A$ pair of tangents is drawn from every point on the line $3x + 4y = 12$ to the circle $x^2 + y^2 = 4$. Their variable chord of contact always passes through a fixed point whose coordinates are:

The common chord of the circles $x^{2}+y^{2}-4x-4y=0$ and $2x^{2}+2y^{2}=32$ subtends at the origin an angle equal to

The equation of the circle whose diameter is the common chord of the circles $x^2+y^2-3x+y-10=0$ and $x^2+y^2-x+2y-20=0$ is