calculus – Using the parameterization for a curve in the xy-plane to calculate the line integral

My question is:

Find a parameterization for the curve in the $xy$-plane given by the parabola with equation $x = y^2.$

Using this, calculate the line integral $int_C mathbf{F}(x)cdot ds$, where $C$ is the curve given by the parabola $x = y^2$ from $(0, 0)$ to $(9, 3)$, and $mathbf F$ is the vector-valued function (or vector field) $mathbf{F}(x,y) = (x^2,y^2) = x^2mathbf{i}+y^2mathbf{j}$.

I understand what the question is asking for but I have no idea where to begin and how to proceed. Would extremely appreciate any help!

calculus – Normal line calculation from a given surface to the xy-plane

Question: Suppose you head toward the $xy$-plane from the surface $x^2+y^2-z^2=-1$ at the point $(1, 1, sqrt{3})$ by following the normal line to the surface at that point. What are the $x$ and $y$ coordinates at which you will hit the $xy$-plane?$

My attempted Solution: I know that the normal line has the parametric equation

$$r(t) = <1+2t, 1+2t, sqrt{3}+2sqrt{3}t>$$
but I’m unsure of how to find the $xy$ coordinates at which this line hits the $xy$ plane. I tried setting $z=0$ and having $sqrt{3}+2sqrt{3}t = 0$. In this case, $t=-1/2$. Solving for $x$ and $y$, they are somehow also both zero.

Could someone please show me how this is done? Thanks!