Suppose that there is line $l$ that is tangent to an ellipse $A$ at point $\,P\,$.
The ellipse has the foci $F'$ and $F$.
One then creates two lines – each from each focus to the tangency point $\,P\,$ .
What I want to prove is that the acute degree formed at $P$ between $l$ and the line segment $F'P$ equals the acute degree formed between $l$ and the line segment $FP$ .
How would I be able to prove this?
(ellipse has a horizontal axis as a major axis.)
Edit: line $l$ and the corresponding $\,P\,$ can be set arbitrarily (they just need to meet the aforementioned condition), so what I want to prove is for all possible cases.
Best Answer
Required to prove that the acute angles made by each foci to the tangent are equal