freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-246-tangents-to-an-ellipse.english.md

---
id: 5900f4621000cf542c50ff75
challengeType: 5
title: 'Problem 246: Tangents to an ellipse'
---

## Description
<section id='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)<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?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler246()</code> should return 810834388.
    testString: assert.strictEqual(euler246(), 810834388, '<code>euler246()</code> should return 810834388.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler246() {
  // Good luck!
  return true;
}

euler246();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>