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Question 516578: A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep. Sketch the paraboloid.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A cable TV receiving dish is in the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep. Sketch the paraboloid.
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I don't have the means to draw a sketch, but I can describe the parabola for you:
Draw a parabola which opens upwards with the vertex at (0,0), one end at (-3,2) and the other at (3,2).
Equation of the parabola: x^2=4py
Location of the receiver will be p-ft from the vertex on the axis of symmetry, x=0.
Using one of the points (3,2) to solve for p.
3^2=4p*2
9=8p
p=9/8 ft
ans:
The receiver will be placed at 9/8 ft above the vertex on the axis of symmetry.
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