The equation of the circle with centre on the $x$-axis,radius $5$ and passing through the point $(2, 3)$ is:

The radius of the circle $2 x^2 + 2 y^2 - 3 x + 2 y - 1 = 0$ is $.......$ units.

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 Cartesian equation of the curve given by $x = 6 \cos \theta$ and $y = 6 \sin \theta$ is

Find the equation of the circle passing through $(0,0)$ and making intercepts $a$ and $b$ on the coordinate axes.

An equilateral triangle whose two vertices are $(-2, 0)$ and $(2, 0)$ and which lies in the first and second quadrants only is circumscribed by a circle. Find the equation of this circle.