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 length (in units) of the common chord of the circles $x^2+y^2+2x+3y+1=0$ and $x^2+y^2+4x+3y+2=0$ is:

If the chord of contact of tangents from a point $A$ to a given circle passes through $B$,then the circle with $AB$ as a diameter will . . . . . .

If $m$ is the slope and $P(8, \beta)$ is the midpoint of a chord of contact of the circle $x^2+y^2=125$,then the number of values of $\beta$ such that $\beta$ and $m$ are integers is

If the line $4x + 4y - 11 = 0$ intersects the circle $x^2 + y^2 - 4x - 6y + 4 = 0$ at $A$ and $B$,then the point of intersection of the tangents drawn at $A$ and $B$ is

The circles $x^2+y^2-2x-4y-4=0$ and $x^2+y^2+2x+4y-11=0$: