A tangent and its normal in an arbitrary point on an ellipse with eccentricity e. The focal points are also shown. What is the minimum value of blue : red in terms of e?
Scroll down for a solution to this problem.
Solution
The minimal blue : red is (1-e)/(1+e).

This proof makes use of the fact that the normal bisects the angle between tangency point and focal points (or Focus-to-focus reflection property).
