Continuity of multivariable function at point

Question

I have to determine whether $$f(x,y)=\frac {x^4-y^4}{x^2+y^2}$$ is continous (or can be made continous) at $(x_0,y_0)=(0,0)$ or not, as far as it can be determined, using $y=mx$ only. Normally I'm ok with solving problems like this. But I am slightly puzzled as to what to do this time since $f(0,0)$ is undefined and $f$ can only be continuous if $$\lim\limits_{(x,y) \to (x_0,y_0)} f(x,y)=f(x_0,y_0)$$ How would I go about solving a problem like this?

Answer 1

HINT: we have $$x^4-y^4=(x^2+y^2)(x^2-y^2)$$