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 8 meters.

If the telescope is 1 m deep and 8 m wide, how far is the focus from the vertex?

I will post a pic in a second.

Answer 1

@Loser66

Answer 2

well a basic form of the parabola is

\[(x - h)^2 = 4a(y - k)\]

(h, k) is the vertex and a is the focal length



so the vertex is at the origin so the equation is

\[x^2 = 4ay\]

substitute a point from the curve (4, 1) into the equation to find the focal length

\[4^2 = 4 \times 1 \times a\]

ad the the focus is a units about the vertex

hope it helps