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A field Microphone has a parabolic cross section and is 18 inches deep.
The focus is 4 inches from the vertex. Find the width of the microphone.
Let's consider its cross-section to be a parabola with vertex at the
origin and opening to the right. Then its equation is
y² = 4px
where p is the distance from the vertex to the focus. This is given
to be p = 4. So the equation is
y² = 4(4)x
or
y² = 16x
which has this graph:
To find the top and bottom points of the microphone,
we substitute 18 for x in the equation:
y² = 16x
y² = 16(18)
___
y = ±Ö288
_____
y = ±Ö2·144
_
y = ±12Ö2
_
So the top point is (18,12Ö2) and the bottom point
_
is (18,-12Ö2)
_
So the width of the microphone is 24Ö2 or about 33.94 inches.
Edwin
