The equation of a circle passing through the point $(4, 5)$ and having the centre at $(2, 2)$ is

Let the abscissae of the two points $P$ and $Q$ be the roots of $2x^{2}-rx+p=0$ and the ordinates of $P$ and $Q$ be the roots of $y^{2}-sy-q=0$. If the equation of the circle described on $PQ$ as diameter is $2(x^{2}+y^{2})-11x-14y-22=0$,then $2r+s-2q+p$ is equal to

The equation of the concentric circle,with the circle $C_1$ having equation $x^2+y^2-6x-4y-12=0$ and having double the area compared to the area of $C_1$,is

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ and having its centre at $(0, 3)$ is

Circles are drawn through the point $(2, 0)$ to cut an intercept of length $5$ units on the $x$-axis. If their centres lie in the first quadrant,then their equation is

If the sides of a rectangle are given by the equations $x=-2, x=6, y=-2, y=5$,then the equation of the circle,drawn on the diagonal of this rectangle as its diameter,is