I think I have found out some property of an ellipse. Define the following:
- The point $P$ belongs to the ellipse.
- The tangent line $\ell$ goes through $P$.
- The point $F$ is one of the foci.
- The line $m$, through $F$, is perpendicular to the line $\ell$ at point $I$.
- $A$ and $B$ are the vertices of the ellipse (that is, the endpoints of the major axis).
In this case,
The $\angle AIB$ is always $\pi/2$. (I think.....)
But I didn't prove yet...
- Is it true?
- Could anybody give me some advice?
Thanks in advance.
Edit1 For jmerry
Edit2 For jmerry
Really thanks, makes me fun!