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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

Sagot :

Answer:

D) [tex]x^{2} =8y[/tex]

Step-by-step 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 [tex](x-h)^2=4p(y-k)[/tex] where [tex](h,k)[/tex] is the vertex of the parabola and [tex](h,k+p)[/tex] 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 [tex](0,0)[/tex] at the origin, then the focus point is [tex](0,0+p)[/tex] where [tex]p=2[/tex]. Therefore, the equation that models a cross section of the dish is [tex]x^{2} = 8y[/tex].

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