Tangents to an ellipse (noch nicht übersetzt)

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.

The construction of the points of the ellipse is shown below.

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 t₁ and t₂ to the ellipse are drawn.
Let the points where t₁ and t₂ touch the ellipse be R and S.

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