The equation of the circle with centre $(2, -3)$ and touching the $X$-axis is

Find the equation of the circle which passes through the origin and cuts off intercepts of $-2$ and $3$ on the $x$ and $y$ axes,respectively.

The centre and radius of the circumcircle of the triangle formed by the lines $2x+3y=10$,$y=x$ and the $X$-axis are respectively:

The equation of the circle passing through the points $(1, \sqrt{2})$,$(7, \sqrt{2})$,and $(1, 3)$ 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 parametric equations of the circle $x^2+y^2-6x-2y+9=0$ are