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Question 1091795: Parabola
The Lovell Telescope is a radio telescope located at the Jodrell Bank Observatory in Cheshire, England. The dish of the telescope has the shape of paraboloid with diameter of 250 feet. The distance from the vertex of the dish to its focus is 75 feet.
A. Find an equation of a cross section of the paraboloid that passes through the vertex of the paraboloid. Assume that the dish has its vertex at (0,0) and vertical axis of symmetry.
B. Find the depth of the dish. Round to the nearest foot
Answer by ikleyn(52798) (Show Source):
You can put this solution on YOUR website! .
The Lovell Telescope is a radio telescope located at the Jodrell Bank Observatory in Cheshire, England. The dish of the telescope
has the shape of paraboloid with diameter of 250 feet. The distance from the vertex of the dish to its focus is 75 feet.
A. Find an equation of a cross section of the paraboloid that passes through the vertex of the paraboloid.
Assume that the dish has its vertex at (0,0) and vertical axis of symmetry.
B. Find the depth of the dish. Round to the nearest foot
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If you read the lesson
- Parabola definition, canonical equation, characteristic points and elements
in this site, you will learn that if you write the canonical equation of a parabola in the form
y = , (1)
then the distance from the parabola's vertex (0,0) to the parabola's focus (focal distance) is .
So, if in your parabola the focal distance is 75 ft, it means that in your equation (1) = 75.
Hence, p = 150, 2p = 300, and the equation of your parabola is
y = .
The depth of the dish is = = = 52.083 ft.
I answered all your questions.
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I have a gift for you.
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The gift is this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic
"Conic sections: Parabolas. Definition, major elements and properties. Solved problems".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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To learn more about the Lovell Telescope see this Wikipedia article
https://en.wikipedia.org/wiki/Lovell_Telescope
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