SOLUTION: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at th

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at th      Log On


   

Question 1204101: A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 84 feet across at its opening and 7 feet deep at its center. Find the equation of the parabola.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Working in 2 dimensions, let the origin of the graph of the parabola be the vertex. The equation is then of the form y=ax%5E2.

The edges of the dish are at the points (-42,7) and (42,7). Determine the value of the coefficient a using either of those two points.

7=a%2842%5E2%29
a=7%2F42%5E2=1%2F%2842%2A6%29=1%2F252

ANSWER: y=%281%2F252%29x%5E2