The centre and radius of the circle $x^2+y^2+8x+10y-8=0$ respectively are

The equation of the circle which touches both the axes and whose radius is $a$ is

The equation of a circle whose centre lies at the point $(-2, 1)$ and which passes through the point $(4, 3)$ is:

The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is

If the equation of the circle passing through the point $(8,8)$ and having the lines $x+2y-2=0$ and $2x+3y-1=0$ as its diameters is $x^2+y^2+px+qy+r=0$,then $p^2+q^2+r=$

In $\triangle ABC$,$\angle A = 90^{\circ}$ and the coordinates of points $B$ and $C$ are $(2, -4)$ and $(1, 5)$. Then the equation of the circumcircle of $\triangle ABC$ is