Parabola Question - Golden Gate Bridge?

Question

The towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280 meters apart and rise 160 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers.

Coordinates for tower: (640, 160)

1. What is the height of the cable 200 meters from a tower? Round to the nearest meter.

2. Use this problem to explain why mathematics can be an evolving discipline, interrelated with human culture, and its connections to other disciplines.

Answer 1

y = px^2
160 = p(640)^2
p = 160/640^2 = 1/2560
640 - 200 = 440 meters from the center
y = (1/2560)(440)^2 = 75.625 = 76meters