Question

Given a parabolic archway that is 20 meters high at the vertex and has a width of 8 meters when the height is 16 meters:

a. What is the value of P in this situation?
b. How wide is the archway at ground level?
c. What is the equation of the directrix?

Answer 1

a. In this situation, the value of P is 5.

b. The width of the archway at ground level is 16 meters.

c. The equation of the directrix is y = -5.

Step-by-step explanation:

a. For a parabolic archway with the given parameters, the value of P in the general form of a parabola y = a(x-h)^2 + k is 5.

b. The width of the archway at ground level can be found by considering the horizontal distance between the two points where the height is 16 meters, resulting in a width of 16 meters.

c. The equation of the directrix for a parabola in the form y = a(x-h)^2 + k is y = k - P, where P is the distance between the vertex and the focus. In this case, the directrix is y = -5.