SOLUTION: A satellite dish has a shape called paraboloid so that its cross-sections through its center (lowest point) are parabolas, all having the same focus. Radio signals sent to it bounc

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A satellite dish has a shape called paraboloid so that its cross-sections through its center (lowest point) are parabolas, all having the same focus. Radio signals sent to it bounc      Log On


   

Question 1169034: A satellite dish has a shape called paraboloid so that its cross-sections through its center (lowest point) are parabolas, all having the same focus. Radio signals sent to it bounce off the surface and are reflected to the focus. The receiver is then placed at the focus. If the satellite dish is 3 meters across and 0.625 meters deep at its center, how far should the receiver be from the center. solution please
Answer by ikleyn(52781) About Me  (Show Source):
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A satellite dish has a shape called paraboloid so that its cross-sections through its center
(lowest point) are parabolas, all having the same focus. Radio signals sent to it bounce off
the surface and are reflected to the focus. The receiver is then placed at the focus.
If the satellite dish is 3 meters across and 0.625 meters deep at its center,
how far should the receiver be from the center. solution please
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For solving such problems, write an equation of the parabola in the cross-section
in the form

    y = %281%2F%284p%29%29%2Ax%5E2.    (1)


The advantage of writing in this form is the fact that then "p"
is the distance from the parabola vertex to its focus.


So, now our task is to find value of "p" from the given data.


The fact that "the satellite dish is 3 meters across and 0.625 meters deep at its center"
means that y = 0.625 meters at x = 3/2 = 1.5 meters.


So, we substitute this data into equation (1), and we get

    0.625 = %281%2F%284p%29%29%2A1.5%5E2.


It gives

    p = %281%2F4%29%2A%28%281.5%5E2%29%2F0.625%29 = 0.9 m.


Thus, the distance from the vertex to the receiver is 0.9 meters.    ANSWER

Solved.