Pre-Calculus
Unit 10 WS 10-2 Parabola Applications
Name:
1. A satellite dish is shaped like a parabola. The signals that emanate from a satellite strike the
surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10
feet across at its widest opening and is 4 feet deep at its center, at what position should the receiver
by placed? (Hint: Where should the focus point be placed?)
2. Your family just purchased a satellite dish to be mounted on your house. The technician is there
to install it. The new dish is a parabola dish that is 3 feet wide and 18 inches deep. The receiver is
located 12 inches from the base inside the dish. Are you getting optimum reception from your new
purchase? Explain.
3. The receiver in a parabolic television dish antenna is 4.5 feet from the vertex and is located at
the focus. Write an equation for a cross section of the reflector. Choose your vertex wisely!
4. The mirror of a flashlight is a parabolic with its diameter of 6 cm and depth of 2cm. How far
from the vertex should the filament of the light bulb be positioned so the beam will run parallel to
the axis of the mirror?
6cm
, 13
5. A bridge with a supporting parabolic arch spans 60 feet with a 30 feet wide road passing under
the bridge. If the minimum clearance is 16 feet, what is the maximum clearance? (Hint: Quadratic
Regression)
6. A suspension bridge is shown below. The main cables are 600 feet apart. The cables attach to
the towers at a height of 110 feet above the roadway and are 10 feet above the roadway at their
lowest points. If the vertical support cables are at 50 foot increments along the roadway, what is the
length of the cables closest to the towers?
!
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7. The picture below shows the cross section view of a new road that is 38 feet wide and is 0.5 feet
high at its center. The shape is parabolic. The design allows for proper drainage of rain-water.
Write an equation for the cross section parabola assuming the origin is at the center of the road.
Based on the information given at what distance from the center of the road, has the height dropped
by 3 inches?
N
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0.5 feet