Graph:
[tex]\left(x^2+y^2-1\right)^3=x^2y^3[/tex]If we replace x with -x, we get the very same expression. This means the function is even, i.e., it's symmetric with respect to the y-axis.
We only have to use values of x greater or equal to 0 and reflect the graph over the y-axis.
For x = 0:
[tex]\left(y^2-1\right)^3=0[/tex]We get y = 1 and y = -1
For x = 1:
[tex]\begin{gathered} \left(y^2\right)^3=y^3 \\ \\ Or: \\ \\ y^6=y^3 \end{gathered}[/tex]Which gives y = 0, y = 1
For x = 0.5
[tex]\left(y^2-0.75\right)^3=0.25y^3[/tex]Which gives y = 1.24 and y = -0.6
You can add more points as desired and have a better graph.
Below is the graph:
