Answer to Question #156880 in Analytic Geometry for Rosette Robles

Question

Suspension bridge are known to be normal around the world especially in developed countries. These bridges usually have towers of some sort and cables, both of which have great importance in the integral stability of the bridge. A STEM student makes some plans for his project on a suspension bridge . He first tries to draw his model.The two towers are 12 meters high and 20 meters apart (10 meters away each from the origin in the center), and the cable he drew between and from the top of the two towers are of course, parabolic. The lowest point of tge cable is 3 meters above the origin. He shows this model to his teacher, and the teacher asks him" what is the vertical distance from the road to the cable at 5 metersaway from the center?" What is the answer toTeacher's question?

Answer 1

Since the curve is parabola, then the standard equation is

$y=ax^2+bx+c$

The the lowest point of tge cable is 3 meters above the origin, what means that it is in (0;3). Then

$x=-b/2a = 0 \implies b=0$

$c=3$

Than we have one of the points on parabola (10;12), it helps us define a:

$12=100a+3$

$100a=9$

$a=0.09$

So the equation of this parabola will look like:

$y=0.09x^2+3$

Using the coordinate of needed point is x=5, so we can find y:

$y=0.09*25+3=5.25$

Finaly the answer is 5.25 meters.