The centre of the circle $r^2-4r(\cos \theta+\sin \theta)-4=0$ in Cartesian coordinates is

The equation of the circle passing through the origin and cutting intercepts of length $3$ and $4$ units from the positive axes is:

The circle $x^2 + y^2 + 6y = 0$ touches which of the following?

If the line $3x - 2y + 6 = 0$ meets the $X$-axis and $Y$-axis at points $A$ and $B$ respectively,then the equation of the circle with radius $AB$ and center at $A$ is

Find the equation of the circle with center $(2, 1)$ and touching the $X$-axis.

The circle $x^2+y^2-8x-12y+\alpha=0$ lies in the first quadrant without touching the coordinate axes. If $(6, 6)$ is an interior point to the circle,then