Find the equation of the circle with centre $(-2, 3)$ and radius $4$.

$A$ circle is drawn with the $y$-axis as a tangent and its center at the point which is the reflection of $(3, 4)$ in the line $y = x$. The equation of the circle is:

If the lines $x+2y-5=0$ and $2x-3y+4=0$ lie along diameters of a circle of area $9\pi$,then the equation of the circle is

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

The lines $2x - 3y = 5$ and $3x - 4y = 7$ are the diameters of a circle of area $154$ square units. The equation of the circle is

If a circle passing through $(4, -2)$ is concentric with the circle $x^2 + y^2 - 2x + 4y + 20 = 0$,then find the value of $c$ for the circle $x^2 + y^2 - 2x + 4y + c = 0$.