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

The abscissae of the two points $A$ and $B$ are the roots of the equation $x^2+2ax-b^2=0$ and their ordinates are roots of the equation $y^2+2py-q^2=0$. Then the equation of the circle with $AB$ as diameter is given by

Find the equation of a circle passing through the origin and making intercepts of length $5$ on both axes.

Find the equation of the circle which passes through the points $(2, -2)$ and $(3, 4)$ and whose centre lies on the line $x + y = 2$.

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

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