A radio telescope in the Very Large Satellite Array at Socorro, New Mexico, has the shape of a parabolic (The cross section of the dish is a parabola). It is 12 feet deep at its center and has a diameter of 82 feet.

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Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 43E: By definition, an ellipse is the locus of points whose sum of distances from two fixed points F1 and...
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A radio telescope in the Very Large Satellite Array at Socorro, New Mexico, has the shape of a parabolic dish
(The cross section of the dish is a parabola). It is 12 feet deep at its center and has a diameter of 82 feet.
Figure 1
Figure 2
Using a cross-section of the parabola as a guide, with the bottom of the base supporting the
satellite located at the origin, determine the coordinates that would represent the vertex of
the dish if the dish is mounted 50 feet off the ground and facing upward (see figure 2).
NEATLY sketch and label a diagram of the cross section of the satellite as you would place it on
a coordinate system including a point on the parabola, and an arbitrary location for the receiver.
To the nearest foot, determine how far above the vertex the receiver is placed in order
to "catch" all of the radio waves that hit the dish. Then, write the equation that models the cross
sectional shape of the dish itself.
Rec. length above vertex:
Equation:_
To verify the receiver is mounted correctly, workers use the location of the directrix, a point on
the edge of the dish and the coordinates for the receiver. By using the definition of a
parabola they can determine if the receiver is located correctly.
If the calculations using the information above are within one tenth of a foot of being exact, the
receiver is considered to be located correctly. Verify the placement you found in problem 2 is
correct.
In order to receive the best quality signal from a certain radio wave, the dish is tilted
so that the axis of symmetry of the satellite runs through the point of verification on the directrix.
To the nearest tenth of a degree, determine how much the satellite was tilted from pointing
straight up.
Transcribed Image Text:A radio telescope in the Very Large Satellite Array at Socorro, New Mexico, has the shape of a parabolic dish (The cross section of the dish is a parabola). It is 12 feet deep at its center and has a diameter of 82 feet. Figure 1 Figure 2 Using a cross-section of the parabola as a guide, with the bottom of the base supporting the satellite located at the origin, determine the coordinates that would represent the vertex of the dish if the dish is mounted 50 feet off the ground and facing upward (see figure 2). NEATLY sketch and label a diagram of the cross section of the satellite as you would place it on a coordinate system including a point on the parabola, and an arbitrary location for the receiver. To the nearest foot, determine how far above the vertex the receiver is placed in order to "catch" all of the radio waves that hit the dish. Then, write the equation that models the cross sectional shape of the dish itself. Rec. length above vertex: Equation:_ To verify the receiver is mounted correctly, workers use the location of the directrix, a point on the edge of the dish and the coordinates for the receiver. By using the definition of a parabola they can determine if the receiver is located correctly. If the calculations using the information above are within one tenth of a foot of being exact, the receiver is considered to be located correctly. Verify the placement you found in problem 2 is correct. In order to receive the best quality signal from a certain radio wave, the dish is tilted so that the axis of symmetry of the satellite runs through the point of verification on the directrix. To the nearest tenth of a degree, determine how much the satellite was tilted from pointing straight up.
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