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Question 170004: A parabolic satellite television antenna has a diameter of 6 feet and is 1.6 feet deep. How far is the focus from the vertex?
I have tried every formula that I can think of to get this one to work out correctly for me and I'm coming up short.
Please help.
Thank you in advance
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A parabolic satellite television antenna has a diameter of 6 feet and is 1.6 feet deep. How far is the focus from the vertex?
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Draw the parabola on an xy coordinate grill.
Put the vertex at (0,1.6)
Then the parabola will meet the x-axis at (-3,0) and (3,0)
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So the equation of the parabola will be y = -x^2 + 1.6
or x^2 = -y - 1.6
or x^2 = -(y+1.6)
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This has the form x^2 = 4p(y-k), so 4p = -1 and p = -1/4
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The distance from the vertex to the focus is p so the
focus is at y = 1.6-(1/4) = 1.6-0.25 = 1.375
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Ans: the focus is (1/4) ft. from the vertex.
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Cheers,
Stan H.
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