The points where the circle $x^2+y^2-3x-4y+2=0$ cuts the $x$-axis 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

The equation of a circle passing through $(-6, 3)$ and touching both the coordinate axes is

Find the equation of the circle with centre $(-a, -b)$ and radius $\sqrt{a^{2}-b^{2}}$.

The abscissae of two points $P$ and $Q$ are the roots of the equation $2x^2 + 4x - 7 = 0$ and their ordinates are the roots of the equation $3x^2 - 12x - 1 = 0$. Then the centre of the circle with $PQ$ as a diameter is

The polar equation of the circle with centre $\left(2, \frac{\pi}{2}\right)$ and radius $3$ units is :