Given a circle $c$ with centre $M$ and radius $r$ and a point $G$ such that $d(G, M) <r$,thelocusofthepointsthatareequidistantfrom$c$and$G$formanellipse.
Given are the points $M(-2000, 1500)$ and $G(8000, 1500)$.
Given is also the circle $c$ with centre $M$ and radius $15\\,000$.
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 $S$.
<imgclass="img-responsive center-block"alt="circle c with the centre M, radius 15000, and point P outsie of ellipse e; from point P two tangents t_1 and t_2 are drawn to the ellipse, with points touching ellipse are R and S"src="https://cdn.freecodecamp.org/curriculum/project-euler/tangents-to-an-ellipse-2.gif"style="background-color: white; padding: 10px;">
For how many lattice points $P$ is angle $RPS$ greater than 45°?