College Algebra & Trigonometry, 2018a

5.3. APPLICATIONS OF THE PARABOLA 285
11) The parabolic mirror for the Mount Palomar observatory telescope is 200
inches in diameter and the mirror is 3.75 inches deep at the center. How far from
the center of the mirror is the focal point where the light is reflected?
12) A reflecting telescope contains a mirror in the shape of a paraboloid. If
the mirror is 5 inches across at the opening and 2 inches deep, how far from the
vertex at the bottom of the mirror is the focal point?
13) The cables of a suspension bridge are in the shape of a parabola. The towers
of the bridge that support the cable are 500 ft. apart and 80 ft. tall. If the
cables are 15 ft. above the roadway at the center of the bridge mid-way between
the towers, how high is the cable 100 ft. from the center of the bridge?
14) The cables of a suspension bridge are in the shape of a parabola. The towers
of the bridge that support the cable are 2000 ft. apart and 400 ft. tall. If the
cables are 25 ft. above the roadway at the center of the bridge mid-way between
the towers, how high is the cable 500 ft. from the center of the bridge?
15) A flashlight reflector housing in the shape of a paraboloid is 4 inches deep
and 4 inches across at its widest point. How far from the vertex at the bottom of
the housing should the light source be placed?
16) A flashlight reflector housing in the shape of a paraboloid is 8 inches in
diameter with the light source placed 1 inch from the vertex at the bottom of the
housing. How deep should the housing be for the light source to be placed at the
focal point?