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A parabolic searchlight is 5ft across its opening. If the light source is located 2ft from the base
along the axis of symmetry, how deep (in feet) is the searchlight?
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The diameter of the searchlight is 5 ft at the opening.
From the general theory, if the focal distanse (the distance from the parabola vertex to the focus of the parabola) is p units,
then the equation of the parabola is y = .
In our case, the focal distance is 2 feet (given), i.e. p = 2.
HENSE, the parabola equation is y = , or y = .
THEREFORE, at x= 2.5 ft (radius of the opening, given), y = = = 0.78125 ft.
ANSWER. The searchlight is 0.78125 ft deep.
Solved.