The abscissac of two points A and B are the roots of the equation $x^2+2ax-b^2=0$ and their ordinates are the roots of the equation $x^2+2px-q^2=0$.Find the equation and the radius of the circle with AB as diameter.

Question

$\begin{array}{1 1}(a)\;x^2+y^2-(\alpha+\beta)x-(y+\delta)y+\alpha \beta+y\delta=0,\sqrt{a^2+p^2+b^2+q^2}\\(b)\;x^2+y^2+(\alpha+\beta)x-(y+\delta)y+\alpha \beta+y\delta=0,\sqrt{a^2-p^2+b^2-q^2}\\(c)\;x^2+y^2-(\alpha+\beta)x-(y+\delta)y-\alpha \beta-y\delta=0,\sqrt{a^2-p^2-b^2-q^2}\\(d)\;\text{None of these}\end{array}$