Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For some fixed $a,b \in \mathbb{R}$, $y = b\sqrt{\frac{x^2}{a^2}-1}$ is supposed to plot the boundary of an ellipse in $\left[0,a\right]$. I came up with that function but it has the defect that it runs into imaginary numbers for $x < a$. I would like to calculate the area of the ellipsis by quadrupling the integral in $\left[0,a\right]$. Would you mind giving me some advice on how to deal with the imaginary part? Maybe there's some way of avoiding it altogether (by using a slightly different function).

share|improve this question
$y = b\sqrt{\frac{x^2}{a^2}-1}$ is a hyperbola. You probably want to plot $y = b\sqrt{1-\frac{x^2}{a^2}}$. –  Sidharth Iyer May 12 '12 at 9:40
Welcome to math.SE: If this is homework, please add the [homework] tag; people will still help, so don't worry. –  Américo Tavares May 12 '12 at 18:51

Your Answer


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

Browse other questions tagged or ask your own question.