Answer:
The width of the spotlight is 20 inches
Step-by-step explanation:
The location of the bulb = 2.5 inches above the vertex
The height of the spotlight = 10 inches
The width of the spotlight =
The
The height of
The equation of a parabola is given as follows;
(x - h)² = 4p(y - k)
Focus, (h, k + p) = (0, 2.5)
y = k - p
k + p = 2.5
Vertex = (h, k) = (0, 0), therefore, k = 0
p = 2.5
We have;
(x - 0)² = 4p(y - 0)
x² = 4×2.5 × y = 10·y
Therefore, given that y = 10, we have;
x² = 10 × 10 = 100
x = √100 = ±10
The coordinates of the two end points are;
(-10, 10), and (10, 10)
Therefore, the width of the spotlight = the distance between the end points
Given that the y-values are the same, we have
Distance = 10 - (-10) = 10 + 10 = 20 inches
∴ The width of the spotlight = 20 inches.
