Partial Derivatives & the Gradient · Hard problem

Consider $f(x,y) = \dfrac{x^{2}y}{x^{4}+y^{2}}$ for $(x,y)\ne(0,0)$. Along every straight line through the origin, $f\to0$. Find the value that $f$ approaches instead along the parabola $y=x^{2}$ as $x\to0$ (showing the overall limit at the origin does not exist).