Math Help - Limits

1. Limits

I need some guidance how to solve the following problem (I have no idea how to get started so any help or explanation would be greatly appreciated):

Question:

Show that if C is any straight line through (0,0) then $\lim_{(x,y) \to (0,0)}$ along C exists and equals 1.

2. To get started, you may use the fact that any straight line through the origin either intersects the parabola at some point and remains above it until $0$ is reached, or lies on $y=0$, in which case $y\le 0$ and $f(x,y)=1$.