Question

Searchlight uses a parabolic mirror to cast a beam of light in parallel rays. The lightbulb is located at the focus of the parabola modeled by y^2 = 36(x - 10). What is the location of the lightbulb?

a) (0, 36)
b) (10, 0)
c) (0, -36)
d) (10, 36)

Answer 1

The lightbulb in a searchlight with a parabolic mirror described by the equation y^2 = 36(x - 10) is located at the focal point of the parabola, which is at the point (10, 0).

Step-by-step explanation:

The student's question is about determining the location of the lightbulb in relation to a parabolic mirror in a searchlight. The equation of the parabola given is y2 = 36(x - 10), which is a standard form of the equation of a parabola y2 = 4px where the focal length, p, is 9, and the vertex of the parabola is at (10,0).

The lightbulb, which acts as the source of light, is always located at the focal point of the parabola. Thus, the lightbulb's location is at the point (10,0), making the answer choice b) (10, 0) correct.