calculus - Why is $f(x,y)$ said to be discontinuous at $(0,0)$?

Why is
$f(x,y)=\begin{cases}
\frac{x^2y}{x^4+y^2}, & \text{if $(x,y)\neq (0,0)$}\\[2ex]
0, & \text{if $(x,y)=(0,0)$}

\end{cases}$ said to be discontinuous at $(0,0)$?

I am supposed to show that this function is not continuous at (0,0), but as $(x,y)$ approaches $(0,0)$, $f(x,y)$ approaches $0=f(0,0)$. So what did I miss here?

Answer

Let $y=x^{2}$. Consider $f(x,x^{2})=\frac{x^{4}}{2x^{4}}=\frac{1}{2}$.So it's not continuous at $(0,0)$. (Even it does not have a limit, you can plug $y=0$)