Your new flashlight uses a parabolic mirror which can be modeled by the equation (x - 2) ² = 5 (y + 1), where x and y are measured in centimeters. You need to place a new light bulb in your flashlight. How far away from the vertex of the parabolic mirror should you place the bulb to ensure a perfect beam of light?

The given equation is

(x - 2) ² = 5 (y + 1).

The given equation for the parabola is in the standard form

(x - h) ² = 4p (y - k)

where

h = 2

4p = 5, so that p = 5/4

k = - 1

The vertex is at

(h, k) or (2, - 1)

The focus is located at

(h, k + p) or (2, - 1 + 5/4) = (2, 1/4)

We should place the bulb at p = 5/4 from the vertex.

Answer: 1 1/4 or 1.25 cm