College Algebra & Trigonometry, 2018a

5.3. APPLICATIONS OF THE PARABOLA 283
Exercises 5.3
1) A satellite dish in the shape of a paraboloid is 10 ft. across and 3 ft. deep.
How far from the vertex at the bottom of the dish should the receiver be placed?
2) A satellite dish in the shape of a paraboloid is 6 ft. across and 2 ft. deep.
How far from the vertex at the bottom of the dish should the receiver be placed?
3) The reflector in a flashlight in the shape of a paraboloid is 2 inches across
and 1 inch deep. How far from the vertex at the bottom of the reflector should
the light source be placed so that the light is reflected straight ahead?
4) The reflector in a flashlight in the shape of a paraboloid is 5 inches across
and 3 inches deep. How far from the vertex at the bottom of the reflector should
the light source be placed so that the light is reflected straight ahead?
5) A car headlight in the shape of a paraboloid has a bulb that is placed 1.25
inches from the vertex at the bottom of the headlight. If the headlight is 6 inches
in diameter, how deep should the headlight be for the bulb to be at the focus of
the paraboloid?
6) A spotlight in the shape of a paraboloid has a bulb that is placed 3 inches
from the vertex at the bottom of the light housing. If the spotlight is 18 inches
in diameter, how deep should the light be for the bulb to be at the focus of the
paraboloid?