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

Let a circle passing through $(2,0)$ have its centre at the point $(h, k)$. Let $(x_c, y_c)$ be the point of intersection of the lines $3x + 5y = 1$ and $(2+c)x + 5c^2y = 1$. If $h = \lim_{c \to 1} x_c$ and $k = \lim_{c \to 1} y_c$,then the equation of the circle is:

The equation of the circle passing through the point $(2, 1)$ and touching the $y$-axis at the origin is:

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

The sides of a rectangle are given by the equations $x=-2, x=4, y=-2$ and $y=5$. Then the equation of the circle,whose centre is the point of intersection of the diagonals,lying within the rectangle and touching only two opposite sides,is

Find the length of the intercept made by the circle on the $y$-axis,if the line segment joining the points $(-4, 3)$ and $(12, -1)$ is the diameter of the circle.