College Algebra & Trigonometry, 2018a

284 CHAPTER 5. CONIC SECTIONS - CIRCLE AND PARABOLA
When a cable, chain or string hangs between two ends, it makes the shape of a
catenary, which is generally described by an equation of the form:
f(x) = ex + e −x
2
However, when the cables of a suspension bridge support the weight of the
roadbed on the bridge, the cables are pulled into the shape of a parabola.
7) The cables of a suspension bridge are in the shape of a parabola. The towers
of the bridge that support the cable are 400 ft. apart and 600 ft. tall. If the cables
touch the roadway at the center of the bridge mid-way between the towers, how
high is the cable 75 ft. from the center of the bridge?
8) The cables of a suspension bridge are in the shape of a parabola. The towers
of the bridge that support the cable are 800 ft. apart and 160 ft. tall. If the cables
touch the roadway at the center of the bridge mid-way between the towers, how
high is the cable 120 ft. from the center of the bridge?
9) A spotlight in the shape of a paraboloid has the light source 2.5 ft. from the
vertex at the bottom of the light. If the depth of the spotlight housing is 4 ft., how
wide should the face of the spotlight be?
10) A flashlight reflector in the shape of a paraboloid has a light source that is
0.5 inches from the vertex at the bottom of the reflector. How deep should the
reflector be if the face of the flashlight is 3 inches in diameter?