Let a,b be positive numbers. Sketch the parabolas

and show that they have a common focus, and that they intersect at right angles.

I was able to show that the focus of each parabola was at the origin by reducing these equations to standard form:

But I don't know how to prove that they intersect at right angles. I got the coordinates as the points of intersection. How do I show that the parabolas cross through these points at right angles to one another? Any help would be appreciated.