The equation $x^2 + y^2 = 0$ denotes

The equation of the circle with radius $5$ and touching the coordinate axes in the third quadrant is:

The radius of the larger circle lying in the first quadrant and touching the line $4x + 3y - 12 = 0$ and the coordinate axes is:

Circles are drawn through the point $(2, 0)$ to cut an intercept of length $5$ units on the $x$-axis. If their centres lie in the first quadrant,then their equation is

The equation of the circle whose diameter lines are $2x + 3y = 3$ and $16x - y = 4$ and which passes through the point $(4, 6)$ is

The sides of a square are $x = 2, x = 3, y = 1$ and $y = 2$. Find the equation of the circle drawn with the diagonal of the square as its diameter.