Question

A radio telescope has a parabolic surface as shown below.

A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 1 meter and its width from left to right is 20 meters.

If the telescope is 1 m deep and 20 m wide, how far is the focus from the vertex?

Answer 1

as shown "below"?

Answer 2

it was a picture but I can't copy and paste it. The description accurately depicts it.

Answer 3

see the [Attach File] blue button?

Answer 4

Thanks! hold on

Answer 5

heheh

Answer 6

it's 1 isn't it

Answer 7

the focus, no

Answer 8

5?

Answer 9

is a parabola, going upwards, the origin is at (0, 0)
so the " focus form" for a parabola will be => \(\huge \bf (x-h)^2=4p(y-k)\)
(h, k) is the vertex of it, in this case (0, 0)
p = focus distance from the vertex

Answer 10

I was thinking that because 4p is focal width, then 20/4 = 5

Answer 11

so, we don't have a "x" and "y" to use there, so we can solve for "p"
so let's find an (x, y)
take a peek at the picture