Hyperbola

Definition: Hyperbola

A hyperbola is a geometric shape $H$ for which there exist two points $F_1,F_2$ such that for each point $P\in H$, the absolute value of the difference in the distances between $P$ and $F_1$ and $P$ and $F_2$ is constant.

$$H=\{P:|d(P,F_1)-d(P,F_2)|=\text{const}\}$$