The equation of the circle whose diameters have the end points $(a, 0)$ and $(0, b)$ is given by:

If $\alpha$ and $\beta$ are the roots of $x^2+2x-3=0$ and $\gamma$ and $\delta$ are the roots of $y^2-y-6=0$,then the equation of the circle having $(\alpha, \gamma)$ and $(\beta, \delta)$ as ends of a diameter is

Let the equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represent a point circle other than the origin. Then which one of the following conditions must hold?

If two vertices of an equilateral triangle are $A(-a, 0)$ and $B(a, 0)$,where $a > 0$,and the third vertex $C$ lies above the $x$-axis,then the equation of the circumcircle of $\Delta ABC$ is:

If $P_1, P_2, P_3$ are the perimeters of the three circles $x^2+y^2+8x-6y=0$,$4x^2+4y^2-4x-12y-186=0$,and $x^2+y^2-6x+6y-9=0$ respectively,then

The centre of the circle given by the parametric equations $x = 2 + 3\cos \theta$ and $y = 3\sin \theta - 1$ is