---
id: 5900f5001000cf542c510012
title: 'Problem 404: Crisscross Ellipses'
challengeType: 5
forumTopicId: 302072
dashedName: problem-404-crisscross-ellipses
---

# --description--

Ea is an ellipse with an equation of the form x2 + 4y2 = 4a2.

Ea' is the rotated image of Ea by θ degrees counterclockwise around the origin O(0, 0) for 0° &lt; θ &lt; 90°.

b is the distance to the origin of the two intersection points closest to the origin and c is the distance of the two other intersection points. We call an ordered triplet (a, b, c) a canonical ellipsoidal triplet if a, b and c are positive integers. For example, (209, 247, 286) is a canonical ellipsoidal triplet.

Let C(N) be the number of distinct canonical ellipsoidal triplets (a, b, c) for a ≤ N. It can be verified that C(103) = 7, C(104) = 106 and C(106) = 11845.

Find C(1017).

# --hints--

`euler404()` should return 1199215615081353.

```js
assert.strictEqual(euler404(), 1199215615081353);
```

# --seed--

## --seed-contents--

```js
function euler404() {

  return true;
}

euler404();
```

# --solutions--

```js
// solution required
```
