The equation of the circle of radius $3$ that lies in the fourth quadrant and touches the lines $x=0$ and $y=0$ is

Find the equation of the circle with radius $5$ whose centre lies on the $x-$axis and passes through the point $(2, 3)$.

The $x$-coordinates of two points $A$ and $B$ are the roots of the equation $x^{2} + 2ax - b^{2} = 0$,and their $y$-coordinates are the roots of the equation $y^{2} + 2py - q^{2} = 0$. Find the radius of the circle with $AB$ as its diameter.

The equation $2x^2 + 2y^2 + 4x + 8y + 15 = 0$ represents

The equation of the circle passing through the points $(1, \sqrt{2})$,$(7, \sqrt{2})$,and $(1, 3)$ is:

Find the equation of the circle with centre $(0,2)$ and radius $2$.