Line Integral Work Done

Question

I have a problem when comes to question 2, I don't know how to put this into parametric form. And I am not sure if this is a parabola. Thanks in advance.

Answer 1

If $y=4x^2$ then the $y$-coordinate of 4 times the square of the $x$-coordinate.

Let the $x$-coordinate be $t$, then the $y$-coordinate of $4t^2$.

Your path is given by $\gamma(t) = (t,4t^2)$, where $0 \le t \le 1$.

The curve $y=4x^2$ is indeed a parabola, with focus $(x,y)=(0,\frac{1}{16})$ and directrix $y=-\frac{1}{16}$.