SOLUTION: I am studing conic sections. I think the equation that could be used for this is: (x-h)^2=4p(y-k) or y= ax^2 +bx+c where P= 1/4a Focus: F(k,k+p) Directrix:y=k-p Does any one kno

Question 114977This question is from textbook Fund of alg and Trig
: I am studing conic sections. I think the equation that could be used for this is: (x-h)^2=4p(y-k) or y= ax^2 +bx+c where P= 1/4a
Focus: F(k,k+p)
Directrix:y=k-p
Does any one know how to solve this problem. I am stumped.
A satellite antenna dish has the shape of a paraboloid that is 10 feet across at the open end and is three feet deep. At what distance from the center of the dish should the reciever be placed to receive the greatest intensity of sound waves. This question is from textbook Fund of alg and Trig

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
let the bottom of the bowl be the origin (0,0)

a cross-section through the center of the bowl gives a parabola with the vertex at the origin, passing through (5,3) and (-5,3)

h and k are zero ___ x^2=4py ___ 5^2=4p(3) ___ 25=12p ___ 25/12=p

the focus (where the receiver should be placed) is 25/12 ft (or 25 inches) above the origin