2018-09-30 22:01:58 +00:00
---
id: 5900f4621000cf542c50ff75
title: 'Problem 246: Tangents to an ellipse'
2020-11-27 18:02:05 +00:00
challengeType: 5
2019-08-05 16:17:33 +00:00
forumTopicId: 301893
2021-01-13 02:31:00 +00:00
dashedName: problem-246-tangents-to-an-ellipse
2018-09-30 22:01:58 +00:00
---
2020-11-27 18:02:05 +00:00
# --description--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
A definition for an ellipse is:
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
Given a circle c with centre M and radius r and a point G such that d(G,M)
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
The construction of the points of the ellipse is shown below.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
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.
2018-09-30 22:01:58 +00:00
For how many lattice points P is angle RPS greater than 45 degrees?
2020-11-27 18:02:05 +00:00
# --hints--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
`euler246()` should return 810834388.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
```js
assert.strictEqual(euler246(), 810834388);
2018-09-30 22:01:58 +00:00
```
2020-11-27 18:02:05 +00:00
# --seed--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
## --seed-contents--
2018-09-30 22:01:58 +00:00
```js
function euler246() {
2020-09-15 16:57:40 +00:00
2018-09-30 22:01:58 +00:00
return true;
}
euler246();
```
2020-11-27 18:02:05 +00:00
# --solutions--
2018-09-30 22:01:58 +00:00
```js
// solution required
```