Hi Sandra.

The distance from the focus to a point on the parabola is the same as the distance from that point to the directrix.

That means that since the distance from the focus to the foot of the bridge is 100 ft (half of 200), then the directrix is 100 ft up as well.

So 100 ft is the distance from the focus to the directrix as well, since the directrix is parallel to the water and above the bridge. But you also know the vertex is halfway between the focus and the directrix, so that is half of 100 ft. So the bridge is 50ft above the water. That answers part (b).

Now think of a graph where the origin is on the water, directly below the center of the bridge. The parabola's vertex is (0, 50) and it passes through the foot of the bridge at (100,0). You can substitute these numbers into y - k = (-1/[4p])(x-h)² to solve for p and complete part (a). Did you forget to put the "p" in your question? I think you meant to write it there.

Hope this helps,
Stephen La Rocque.