conics question (hyperbola)

[annaconda]

Hello,
This question comes from fitzpatrick 4u (EX 4.5), and I was just wondering if someone could help me out?

The question goes:
P is a variable point on the hyperbola x²/a² - y²/b² = 1, and the foci are at S and S'. Prove that the tangent at P bisects angle S'PS

Many thanks in advanced!!!

[RuiAce]

This is the usual reflection property of the hyperbola. You can find it in the 2012 paper, and also the similar version for the ellipse in the 2009 (somewhat recommended) and 2007 paper; all of which have solutions by Terry Lee. (Remember that anything that works for the ellipse can be adapted to work for the hyperbola as well, but it's a bit harder to do so.)

[annaconda]

thanks Rui!!!
I'll check it out