The circle passing through $(1, -2)$ and touching the $x$-axis at $(3, 0)$ also passes through the point

If the lines $3x - 4y - 7 = 0$ and $2x - 3y - 5 = 0$ are two diameters of a circle of area $49\pi$ square units,the equation of the circle is:

The equation of a circle of radius $5$ units touching another circle $x^2+y^2-2x-4y-20=0$ at $(5,5)$ is

If the equation $\frac{K(x + 1)^2}{3} + \frac{(y + 2)^2}{4} = 1$ represents a circle,then $K = $

Let the equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represent a point circle other than the origin. Then which one of the following conditions must hold?

$A$ circle is concentric with the circle $x^2 + y^2 - 6x + 12y + 15 = 0$ and has an area double that of the given circle. The equation of the circle is: