SOLUTION: A satellite dish shaped like a parabola is 12 feet across and 4 feet deep. How high above the base dish should the receiver be placed if it is located at the focus of the parabola?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A satellite dish shaped like a parabola is 12 feet across and 4 feet deep. How high above the base dish should the receiver be placed if it is located at the focus of the parabola?      Log On


   

Question 433509: A satellite dish shaped like a parabola is 12 feet across and 4 feet deep. How high above the base dish should the receiver be placed if it is located at the focus of the parabola?
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Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
picture the parabolic cross-section starting at the origin and extending along the x-axis

the vertex (bottom of the dish) is (6,-4); and the roots are 0 and 12

using the vertex form ___ y = a(x - 6) - 4

0 = a(0 - 6)^2 - 4

4 = 36a ___ a = 1/9

a = 1 / 4p ___where p is the distance from the vertex to the focus

p = 1 / 4a ___ in this case ___ p = 9/4

so the receiver is 9/4 feet above the bottom of the dish