Answer
(a) $x^2=4y, x^2=8y, x^2=16y$ and $x^2=32y$
(b) See graphs and explanations below.
Work Step by Step
(a) Since the vertex is at the origin with focus on the y-axis, we can write the general equation for the parabola as $x^2=4py$ with focus at $y=p$. Given $y_F=1,2,4,8$, we have $p=1,2,4,8$, so the equations are $x^2=4y, x^2=8y, x^2=16y$ and $x^2=32y$ respectively.
(b) See graphs, we conclude that with the increasing of absolute values of the focus, the openings of the parabola become wider.
