Associated Topics || Dr. Math Home || Search Dr. Math

### Points within an Ellipse

```Date: 06/03/2003 at 06:32:27
From: Elly
Subject: Ellipse

My task is to generate points within an ellipse. I did it within a
circle but I couldn't determine a condition for a point to be inside
an ellipse.
```

```
Date: 06/03/2003 at 08:15:52
From: Doctor George
Subject: Re: Ellipse

Hi Elly,

Thanks for writing to Doctor Math.

There are a couple of ways to determine whether a point is inside an
ellipse. If the ellipse is in standard position, a point is inside it
if

x^2   y^2
--- + --- < 1
a^2   b^2

This is similar to determining whether a point is inside a circle.

If the ellipse is not in standard position, or is in 3D space, then
it may be easiest to go back to the definition of an ellipse. An
ellipse is the locus of points such that the sum of the distances
from each point to the two foci equals 2a. Remember that 2a is the
length of the major axis.

If the sum of the distances is less than 2a, then the point is inside
the ellipse. Let's call the foci vectors C1 and C2. A point P is
inside the ellipse if

|P - C1| + |P - C2| < 2a

Does this make sense? Write again if you need more help.

- Doctor George, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 06/04/2003 at 09:07:48
From: Elly
Subject: Thank you (Ellipse)

I did it! :)
Thank you very much.
```
Associated Topics:
College Conic Sections/Circles
High School Conic Sections/Circles

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search