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


Given an ellipse at (0, 0), with height "h" and width "w", what's the "x" coordinate along the perimeter for a given "y" coordinate?

share|cite|improve this question
up vote 6 down vote accepted

An ellipse is in the standard form if its major and minor axes are co-ordinate axes and intersect at origin. This point of intersection is usually called the center of the ellipse.

This is a standard ellipse whose equation is $$ \dfrac{4x^2}{w^2}+\dfrac{4y^2}{h^2}=1$$

Also, notice that, since the curve is symmetric about origin, there are always $2$ $x$- coordinates that satisfy a given $y$-coordinate and vice versa.

$$x=\pm \dfrac{w}{2}\sqrt{1-\dfrac{4y^2}{h^2}}$$ $$y=\pm \dfrac{h}{2}\sqrt{1-\dfrac{4x^2}{w^2}}$$

Now, that you have pointed out to a positive $x$, we can resolve this sign ambiguity and we'll have that, $$\boxed{x=+\dfrac{w}{2}\sqrt{1-\dfrac{4y^2}{h^2}}}$$

share|cite|improve this answer
This raises a question about the factor of $2$ you have included: In his diagram, does $h$ refer to the distance from the top of the ellipse to the bottom, or from the origin to the top? (I really can't tell from the picture) – Eric Naslund Feb 2 '12 at 14:58
@Eric, OP says his/her ellipse is of height "h", and not "2h". So, I thought this was a reasonable interpretation. – user21436 Feb 2 '12 at 15:00
Just tested it. That's exactly what I needed. Thanks! – ElephantHunter Feb 2 '12 at 15:19

The equation for the ellipse will be $$\frac{x^2}{w^2}+\frac{y^2}{h^2}=1.$$

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.