Find the centre and radius of the circle $(x+5)^{2}+(y-3)^{2}=36$.

Find the equation of the circle with centre $(-a, -b)$ and radius $\sqrt{a^{2}-b^{2}}$.

The equation of the circle concentric with the circle $x^2 + y^2 + 8x + 10y - 7 = 0$ and passing through the centre of the circle $x^2 + y^2 - 4x - 6y = 0$ is

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

The ratio of the areas of the concentric circles $x^2+y^2-6x+12y+15=0$ and $x^2+y^2-6x+12y-15=0$ is

Let a circle $C$ have its centre in the first quadrant,intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of $C$ on the line $x + y = 1$ is $\sqrt{14}$,then the square of the radius of $C$ is . . . . . .