If $\theta$ is the angle between the circles $x^2+y^2-4x+2y-4=0$ and $x^2+y^2-2x+4y-11=0$,then $\sin \theta=$

If the equation of the incircle of an equilateral triangle is $x^2 + y^2 + 4x - 6y + 4 = 0$,then the equation of its circumcircle is:

$x^2+y^2+2x-6y-6=0$ and $x^2+y^2-6x-2y+k=0$ are two intersecting circles and $k$ is not an integer. If $\theta$ is the angle between the two circles and $\cos \theta = \frac{-5}{24}$,then $k=$

$A$ circle $C$ touches the $X$-axis and makes an intercept of length $2$ units on the $Y$-axis. If the centre of this circle lies on the line $y=x+1$,then which of the following is a circle passing through the centre of the circle $C$?

$A$ line $l$ meets the circle $x^2+y^2=61$ at points $A$ and $B$. Given that $P(-5, 6)$ is a point such that $PA=PB=10$,find the equation of line $l$.

$A$ line $l$ meets the circle $x^2+y^2=61$ at points $A$ and $B$. If $P(-5, 6)$ is a point such that $PA=PB=10$,then the equation of line $l$ is: