## Tangents to an ellipse

### Problem 246

Published on Friday, 22nd May 2009, 05:00 pm; Solved by 541; Difficulty rating: 80%
A definition for an ellipse is:

Given a circle c with centre M and radius r and a point G such that d(G,M)<r, the locus of the points that are equidistant from c and G form an ellipse.

Given are the points M(-2000,1500) and G(8000,1500).

Given is also the circle c with centre M and radius 15000.

The locus of the points that are equidistant from G and c form an ellipse e.

From a point P outside e the two tangents t_{1} and t_{2} to the ellipse are drawn.

Let the points where t_{1} and t_{2} touch the ellipse be R and S.

For how many lattice points P is angle RPS greater than 45 degrees?