SOLUTION: A satellite dish is in the shape of of a parabolic surface. The satellite dish has a diameter of 12 feet and a depth of 2 feet. How far from the base of the dish should the recei

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A satellite dish is in the shape of of a parabolic surface. The satellite dish has a diameter of 12 feet and a depth of 2 feet. How far from the base of the dish should the recei      Log On


   

Question 1032249: A satellite dish is in the shape of of a parabolic surface. The satellite dish has a diameter of 12 feet and a depth of 2 feet. How far from the base of the dish should the receiver be placed?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The base of the dish is the vertex of parabola. Where to place the receiver would be the focus of the parabola. Imagine or draw a parabola, concave upward, with the vertex at the origin. Half the diameter at a HEIGHT of 2 feet gives the two points (6,2) and (-6,2). You do not know directrix and focus but you do not yet need them.

Standard form equation y=a%28x-h%29%5E2%2Bk and for vertex at origin, y=ax%5E2. You want this in a slightly different form, using p for distance from vertex to either the focus or directrix.

highlight%284py=x%5E2%29-------which is what you would find from deriving the equation if given the focus and directrix.

Use the known point about diameter and "height".
4p%2A2=6%5E2
p=6%2A6%2F%284%2A2%29
highlight%28highlight%28p=3%2F2%29%29

Put the receiver 1.5 feet from the vertex on the concave side of the dish.