Solution
= Solution
By the focal definition of an <ellipse>, the solution set is the ellipse with foci $a$ and $b$. Its centre is $(a+b)/2$, its major axis lies along the line through the foci, and its semiaxes are
$$
\frac c2,\qquad \frac12\sqrt{c^2-|a-b|^2}.
$$
The sketch is consequently a <nondegenerate ellipse> symmetric about both the <focal line> and its <perpendicular bisector>.