Finding a function 2 variables with a certain property : $f(x_0,y_0)=f(x_1,y_1)=0$ and $f>0$ elsewhere

Question

I'm looking for a function $f(x,y)$ of $\mathbb{R}^2$ into $\mathbb{R}$ with global minima at $x_0,y_0$ and $x_1,y_1$. It should respect : $f(x_0,y_0)=f(x_1,y_1)=0$ and $f>0$ elsewhere.

Could you help me plz ?

Answer 1

How about

$$f(x,y)=\left[(x-x_0)^2+(y-y_0)^2\right] \cdot \left[(x-x_1)^2+(y-y_1)^2\right]\;?$$