What is the equation for the cross section of a parabolic TV antenna dish?

[vitaly]

I'm having difficulty with this question. All help is appreciated.

*The cross section of television antenna dish is a parabola and the receiver is located at the focus.

A. If the receiver is located 5 feet above the vertex, assume the vertex is the origin, find an equation for the cross section of the dish.
Okay, I know the vertex is 0,0. The focus is 0, 5. The equation is x^2=4ay.
I don't know where to go from there, or what equation is needed to find the cross section.

 

[vitaly]

Actually, I figured it out. x^2 = 4ay, and a must equal 5 because the focus is (0,5).
That means teh equation is x^2 = 4(5)y or x^2 = 20y.

What I can't figure out is part B:
If the dish is 10 feet wide, how deep is it?
I have never had a question like this before. How do you know how "deep" a dish is?

 

[Kamataat]

So the equation of the parabola is $y=x^2/20$. If it's 10 feet wide and centered at the origin, then it's cross section is between -5 and 5 on the x-axis. So, to find the depth, you need to calculate "y" for x=5... that is, if I understand the question correctly.

- Kamataat

 

[vitaly]

Thank you for the help. I think that's right. Solving for y, it would be 1.25, which is the answer. I just didn't know how to come to it and show my work. Thanks again.