orthogonal curves

orthogonal curves

65–68Two 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.
65. x2 + y2 = r 2, ax + by = 0
66. x2 + y2 = ax, x2 + y2 = by
67. y = cx2, x2 + 2y2 = k

68. y = ax3, x2 + 3y2 = b