Question

SATELLITE DISH Suppose the receiver in a parabolic dish antenna is 2 feet

from the vertex and is located at the focus. Assume that the vertex is at the
origin and that the dish is pointed upward. Find an equation that models a
cross section of the dish.
a. x2 = -8y
b. x2 = 2y
c. x2 = 8y
d. y2 = 8x

Answer 1

D)
`x^(2) =8y`

Explanation:

Because the receiver of the parabolic dish antenna is 2 feet above the vertex, the parabola must be vertical. Therefore, we will use the equation
`(x-h)^2=4p(y-k)` where
`(h,k)` is the vertex of the parabola and
`(h,k+p)` is the focus point. Since we are given that the receiver is 2 feet above the vertex which is located at the focus point and the vertex is
`(0,0)` at the origin, then the focus point is
`(0,0+p)` where
`p=2`. Therefore, the equation that models a cross section of the dish is
`x^(2) = 8y`.