Given points $F_1(-c,0)$ and $F_2(c,0)$, and a number $2a$,the locus of points whose difference of the distances to foci $F_1$ and $F_2$ equals to the constant $2a$ forms a hyperbola. The equation is $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$where $b=\sqrt{c^2-a^2}$. The eccentricity is defined to be $e=\frac{c}a$.