SOLUTION: 2.) NASA is designing a new satellite to go on the international space station. The satellite disk is the shape of a parabola. The satellite will be attached to the station on a po

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Question 1171330: 2.) NASA is designing a new satellite to go on the international space station. The satellite disk is the shape of a parabola. The satellite will be attached to the station on a pole and will place the vertex of the satellite 4 feet away from the surface of the station. The receiver is to be positioned 7 feet above the roof. Write an equation that best models the parabolic cross section of the of the satellite dish.
Answer by greenestamps(13198) About Me  (Show Source):
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The vertex form of the equation of a parabola is

y+=+%281%2F%284p%29%29%28x-h%29%5E2%2Bk

where (h,k) is the vertex and p is the directed distance from the vertex to the focus.

We can (arbitrarily) use the foot of the pole as the origin of our coordinate system; then the vertex is at (0,4).

The receiver is at the focus; it is at (0,7), so p, the distance from the vertex to the focus, is 3.

Then the equation is

y+=+%281%2F12%29x%5E2%2B4