---
id: 5900f4621000cf542c50ff75
title: 'Problem 246: Tangents to an ellipse'
challengeType: 5
forumTopicId: 301893
dashedName: problem-246-tangents-to-an-ellipse
---

# --description--

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)

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?

# --hints--

`euler246()` should return 810834388.

```js
assert.strictEqual(euler246(), 810834388);
```

# --seed--

## --seed-contents--

```js
function euler246() {

  return true;
}

euler246();
```

# --solutions--

```js
// solution required
```