Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have 3 random points in an ellipse. Is it possible to find the radius of the ellipse?

share|cite|improve this question
No. Since there are two circles containing every three points not no a line, you can take any ellipse which isn't a circle and three points on it, then there will be a circle (i. e. another ellipse) through it having different radius. – martini May 2 '12 at 12:40
If your ellipse is axis-aligned, you need four points to uniquely determine it; if not axis-aligned, you need five points. Your problem as it stands is underdetermined. – J. M. May 2 '12 at 12:45
@martini: That's not right. Three points not on a line determine a unique circle. – TonyK May 2 '12 at 13:02
@TonyK Upps ... you are right of course. – martini May 2 '12 at 13:04

The equation of an ellipse whose major and minor axes are parallel to the Cartesian axes is:

$$ \left(\frac{x-x_{0}}{a}\right)^{2}+\left(\frac{y-y_{0}}{b}\right)^{2}=1 $$

As you can see, the equation contains 4 different variables. Therefore, 3 points aren't sufficient to uniquely identify the ellipse.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.