Here's a problem that my teacher specifically assigned to me to make it as hard as possible.

**A ball with a radius of 1 is dropped into a parabolic container whose surface is described by rotating y=x^2 around the y-axis. When the ball comes to rest, how far is its bottom from the bottom of the container?**
(The image above isn't the exact image that's on the problem, but it's an accurate re-creation.)

The image above is missing

**point a** (which is at the center of the circle and on the y-axis. The slanted line going from point a (the center) to the point labeled (x,y) =

**1 **because it's a radius.

Okay, so I'm not 100% sure how to start this problem. Is it even possible to get an exact value, or will I have to find the distance between the two bottoms in terms of x?