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

The height of the telescope of 1 meter and width of 20 meters gives a distance of the focus from the vertex of 25 meters.

Which method can be used to find the distance between the focus and vertex?

Given that the vertex is at the origin, we have;

(h, k) = (0, 0)

The equation of a parabola is presented as follows;

(x - h)² = 4•p•(y - k)

x² = 4•p•y

When x = 10, y = 1

Therefore;

p = 10² ÷ 4 = 25

The focus of the parabola = (h, k + p)

Which gives;

The focus of the parabola = (0, 0 + 25) = (0, 25)

The distance of the focus from the vertex is therefore;

• d = 25 - 0 = 25

• The distance of the focus from the vertex is 25 meters

Learn more about the parts of a parabola here:

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