The equation of the circle with centre $(2,3)$ and touching the line $3x-4y+1=0$ is

Find the equation of a circle whose diameters are $2x - 3y = 5$ and $3x - 4y = 7$ and whose radius is $8$.

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

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

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 $\alpha$ 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