# An Elliptic Identity

An Elliptic Identity

Let E be a point on an ellipse, O its center, F and G its two foci, and P the point on the tangent line to E such that OP is perpendicular to the tangent line. Then the identity is . Drag the point E to see that the identity holds for ellipses of different shapes and sizes.

EF×EG

×=

2

OP

2

a

2

b