--description--

A definition for an ellipse is:

Given a circle $c$ with center $M$ 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 center $M$ 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 $S$.

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

--hints--

tangentsToAnEllipse() should return 810834388.

assert.strictEqual(tangentsToAnEllipse(), 810834388);

--seed--

--seed-contents--

function tangentsToAnEllipse() {

  return true;
}

tangentsToAnEllipse();

--solutions--

// solution required