freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-422-sequence-of-points-on-a-hyperbola.english.md

---
id: 5900f5131000cf542c510025
challengeType: 5
title: 'Problem 422: Sequence of points on a hyperbola'
---

## Description
<section id='description'>
Let H be the hyperbola defined by the equation 12x2 + 7xy - 12y2 = 625.

Next, define X as the point (7, 1). It can be seen that X is in H.

Now we define a sequence of points in H, {Pi : i ≥ 1}, as:
 P1 = (13, 61/4).
 P2 = (-43/6, -4).
 For i > 2, Pi is the unique point in H that is different from Pi-1 and such that line PiPi-1 is parallel to line Pi-2X. It can be shown that Pi is well-defined, and that its coordinates are always rational.
You are given that P3  = (-19/2, -229/24), P4 = (1267/144, -37/12) and P7 = (17194218091/143327232, 274748766781/1719926784).

Find Pn for n = 1114 in the following format:If Pn = (a/b, c/d) where the fractions are in lowest terms and the denominators are positive, then the answer is (a + b + c + d) mod 1 000 000 007.

For n = 7, the answer would have been: 806236837.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler422()</code> should return 92060460.
    testString: 'assert.strictEqual(euler422(), 92060460, "<code>euler422()</code> should return 92060460.");'

```

</section>

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

<div id='js-seed'>

```js
function euler422() {
  // Good luck!
  return true;
}

euler422();
```

</div>



</section>

## Solution
<section id='solution'>

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