Show that the ellipse x = a cos t, y = b sin t, a > b > 0, has its largest curvature on its major axis and its smallest curvature on its minor axis. (As in Exercise 17, the same is true for any ellipse.)

Exercise 17

Show that the parabola y = ax², a ≠ 0, has its largest curvature at its vertex and has no minimum curvature.