Answer to Question #241614 in Analytic Geometry for Barbie

Question

The strings of a horizontal suspension are supporter by two towers 100 feet apart and 25 feet high. Find the parabolic equation (in standard form) with the center of the bridge as the origin. Note: A suspension bridge cable hangs in a parabolic arc when the weight is evenly distributed along horizontal line.

Answer 1

The vertex is $(0,0).$ The standard form of the parabola is

$$y=ax^2$$

Point $(50, 25)$ lies on the parabola

$$25=a(50)^2$$

$$a=0.01$$

The parabolic equation (in standard form) is

$$y=0.01x^2$$