A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x^2=4y around its axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? Express your answer as a fraction or a decimal rounded to two decimal places.

Question

Mathematics

Rosa Riddle

24 February, 12:04

A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x^2=4y around its axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? Express your answer as a fraction or a decimal rounded to two decimal places.

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Answers (1)

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Zachariah Schneider · Answer 1

1.00 inches

Step-by-step explanation:

The distance from vertex to focus is "p" in the quadratic equation ...

x^2 = 4py

In the given equation, p=1. Since units are inches, ...

the bulb should be placed 1.00 inches from the vertex.