Consider an annulus
with the inner radius $a$ and the outer radius $b$, where $0 \leq a \leq b$. Fix one diameter of this annulus. Find the implicit equation for $a$ and $b$ such that the average distance between a point in this annulus and the fixed diameter equals $1$.
The graph of the implicit equation found for $a$ and $b$ is a part of the curve that belongs to a well known family of curves. Describe in detail this curve. (You can do this almost by guessing and using the answers to the previous questions. Formally, you need Math 304 to answer this question.)