Reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. the microphone itself is placed on the focus of the parabola. if the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?

If we impose the parabola on the coordinate system facing to the right, then we can derive its equation. The general form is:
y² = 4ax
where a is the distance of the focus from the vertex.

From the problem, a possible point on the parabola is (30, 30). Substituting to solve for a:
30³ = 4a(30)
a = 7.5

So, the microphone should be put 7.5 inches from the vertex.

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this is a parabola y^2 = 4ax with focus at (a,0)

so plugging in corresponding values of x and y 20^2 = 4a * 20 = 80a

giving a = 400/80 = 5

microphone must be placed 5 inches form the vertex

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