Question

A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x2=3y 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.

Answer 1

3/4 inch

Explanation:

Where p is the distance from the focus to the vertex, the equation of a parabola can be written ...

4py = x^2

The equation given here is ...

3y = x^2

so, we have ...

4p = 3

p = 3/4 . . . . . . divide by 4

The distance from the focus to the vertex is 3/4 inch.