see the link on conic sections in my signature.

Hint: hopefully you see why this makes sense, but the center of the circle is the midpoint of the line segment between the two points given. and the radius is 1/2 the distance between the two points (which you can find by the distance formula)2). Find the equation of the circle with diameter endpoints at [squareroot 2,6] and [-3squareroot 2, -11/4]