Question

(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 bulb should be placed .

Answer 1

Answer:

The coordinates of the point the bulb should be placed is (2, 0.25)

Explanation:

The given equation of a parabola is presented as follows;

(x - 2)² = 5·(y + 1)

The point the bulb should be placed is the focus of the parabolic mirror to ensure a perfect (straight) beam

The general form of the equation of a parabola is (x - h)² = 4·p·(y - k)

The coordinates of the focus of the parabola for p > 0 f = (h, k + p)

By comparison, h = 2, k = -1, and p = 5/4

∴ The coordinates of the focus of the parabola, f = (2, -1 + 5/4)  = (2, 0.25)

The coordinates of the point the bulb should be placed is at the focus, f =  (2, 0.25).