Mathematics

The key insight is that point $B$ (the end of the semi-minor axis) has a special geometric relationship with the foci. Since $B$ lies on the ellipse and $\angle FBF' = 90°$, you can use the distance formula combined with the definition of an ellipse—the sum of distances from any point to the two foci equals $2a$. Set up a right triangle with the foci and $B$, then use the Pythagorean theorem to relate $a$, $b$, and $c$ (where $c$ is the focal distance), which will let you find eccentricity $e = c/a$.

The key insight is that point $B$ (the end of the semi-minor axis) has a special geometric relationship with the foci. Since $B$ lies on the ellipse and $\angle FBF' = 90°$, you can use the distance formula combined with the definition of an ellipse—the sum of distances from any point to the two foci equals $2a$. Set up a right triangle with the foci and $B$, then use the Pythagorean theorem to relate $a$, $b$, and $c$ (where $c$ is the focal distance), which will let you find eccentricity $e = c/a$.