The abscissa of the two points A and B are the roots of the equation `x^2+2a x-b^2=0` and their ordinates are the roots of the equation `x^2+2p x-q^2=0.` Find the equation of the circle with AB as diameter. Also, find its radius.

Answer

`|{:(x^(2)+y^(2)-x_(3)^(2)-y_(3)^(2),x-x_(3),y-y_(3)),(x_(1)^(2)+y_(1)^(2)-x_(3)^(2)-y_(3)^(2),x_(1)-x_(3),y_(1)-y_(3)),(x_(2)^(2)+y_(2)^(2)-x_(3)^(2)-y_(3)^(2),x_(2)-x_(3),y_(2)-y_(3)):}|`