#### Problem 50E

49-52 Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Show that the given families of curves are orthogonal trajectories of each other; that is, every curve in one family is orthogonal to every curve in the other family. Sketch both families of curves on the same axes.

50. $x^{2}+y^{2}=a x, \quad x^{2}+y^{2}=b y$