in a 2D rigid body animation, there are two objects (see Figure 3), a fixed concave supporter (outlined by red curves) whose supporting curve is described by an explicit representation

and an elliptic object whose shape is described by an implicit representation

This description assumes the elliptic object is centered at (0,0). However, since the elliptic object is not fixed, initially in the animation it is placed at (0,H) and starts to fall down due to gravity. It then hits the supporter and eventually reaches a stable equilibrium. When the elliptic object settles stably on the supporter, its center position position is at (0,h). Derive a formula to compute h using the elliptic parameters a and b.

y = x2-1, x E [-1.5, 1.5]