Given the function

$(a)$ Find $f(x,y)=\{\begin{array}{ccc}\frac{x^{2}y}{x^2{y}^2},& (x,y)(0,& 0)\end{array}$

$0,(x,y)=(0,0)$

$\underset{(x,y)(0,0)}{lim}f(x,y)$

along any line $y=kx.$

$($b$)$ Find

$\underset{(x,y)(0,0)}{lim}f(x,y)$

along any parabola

$y=k{x}^2.$