Hello,

I have a question about parametrization of "submanifolds" or curves, respectively.

In particular in the following example:

"Let M $\displaystyle \subset \mathbb{R}^2$ be the set of all points which have the product of their distanes from (-1,0) and (1,0) equal 1."

Give a parametrization of M. Is M a submanifold of dimension 1?

so i thing M={(x,y): $\displaystyle (x^4-2x^2)/(2x^2+2) = -y^4-y^2$}

so i think the curve in $\displaystyle \mathbb{R}$ is like two symmetric loops between $\displaystyle +-\sqrt{2}$.

I don't think thant M is a submanifold because of the point (0,0). But i don't know how i can parametrize M. I never have done this before. How can this be done?

Regards