Inverted Circle?

154 Views Asked by At

The equation I have is

$$\Large x^{\frac23} + y^{\frac23} = 3^{\frac23} $$

I know what the graph looks like, but I don't know how I would find points other than the intercepts mathematically. How would I do that?

1

There are 1 best solutions below

2
On

Try $\begin{cases} x=3\cos^3\theta\\ y=3\sin^3\theta\\ \end{cases}$ or, for rational solutions, $\begin{cases} x=3\left({{2t}\over{t^2+1}}\right)^3\\ y=3\left({{t^2-1}\over{t^2+1}}\right)^3\\ \end{cases}$