I have no idea how this equation: \begin{equation} (x^2 + y^2 - 1)^3 - x^2 y^3 = 0 \end{equation}
Produces this picture:
Can someone provide a general explanation of plotting this function?
I have no idea how this equation: \begin{equation} (x^2 + y^2 - 1)^3 - x^2 y^3 = 0 \end{equation}
Produces this picture:
Can someone provide a general explanation of plotting this function?
The solution set is obviously symmetric with respect to the $y$-axis. Therefore we may assume $x\geq 0$. In the domain $\{(x,y)\in {\mathbb R}^2\ |\ x\geq0\}$ the equation is equivalent with $x^2+ y^2 -1=x^{2/3} y\ ,$ which can easily be solved for $y$: $y={1\over2}\bigl(x^{2/3}\pm\sqrt{x^{4/3}+4(1-x^2)}\bigr)\ .$ Now plot this, taking both branches of the square root into account. You might have to numerically solve the equation $x^{4/3}+4(1-x^2)=0$ in order to get the exact $x$-interval.