# Does a plane curve with polar equation $r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$ have a name?

Does a plane curve with polar equation $$r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$$ where both $\lambda_i>0$ have a name?

It's very similar to hippopede, also known as lemniscate of Booth, but not quite the same: hippopede equation can be written in the same way but with $r^2$ instead of $r$.

Here is how it looks like for $\lambda_2=1$ and $\lambda_1 \in \{\frac{1}{2}, 1, 2, 3, 4, 5\}$:

Update: I realized that in my application it is more natural to put $r^2$ instead of $r$ in the equation above; hence what I appear to be dealing with is a hippopede after all. The family of curves displayed above is likely not to have any name (hard as I tried, I failed to find any).

• I don't know but it is a nice family of curves ! – Claude Leibovici Nov 11 '15 at 10:50
• I don't have a name either. What I can say is that it is a conchoid of a four-leaf rose. – J. M. is a poor mathematician Jul 23 '16 at 16:03
• Out of curiosity, what was your application where this appeared? – gota Jun 6 at 14:19