If and are two points on an Ellipse

(1) 
with Eccentric Angles and such that

(2) 
and and . Then

(3) 
This follows from the identity

(4) 
where is an incomplete Elliptic Integral of the Second Kind, is a complete Elliptic Integral
of the Second Kind, and
is a Jacobi Elliptic Function. If and
coincide, the point where they coincide is called Fagnano's Point.
© 19969 Eric W. Weisstein
19990526