The cross section of a television antenna dish is a parabola. A dish has a receiver that is located at the focus, 4 ft. above the vertex.
Find the equation. (which I did) -- x^2 = 8y
If the dish is 8 feet wide, how deep is it?
so x = +/- 4 if 8 wide
what is y ?
16 = 8 y
y = 2
Wow. Do I just substitute x with 8, and then solve to get y=5?
Oops nevermind, sorry.
No, x is half the width.
To find the depth of the dish, we need to determine the y-coordinate of the vertex of the parabola.
In the equation you provided, x^2 = 8y, we can see that the coefficient of the y-term is 8. The standard form of a parabola equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Comparing the given equation with the standard form, we can determine that a = 8. Since we are given that the dish is 8 feet wide, which means the x-coordinate of the vertex is 0, we substitute the values into the equation and solve for k.
x = 0
0^2 = 8y
0 = 8y
y = 0
Therefore, the vertex of the parabola is (0, 0). The y-coordinate of the vertex represents the depth of the dish. In this case, the depth is 0 ft.
Hence, the dish is not deep, as it has a depth of 0 ft.