a spotlight has A spotlight has a parabolic cross section th

A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the parabolic is the focus? Round answer to two decimal places. A) 0.52 ft B) 0.26 ft C) 0.21 ft D) 0.90 ft

Solution

This parabola opens upward and so it has the form
x^2 = 4Py where P = distance of vertex from focus and vertex at origin (0,0)
Given that parabola is 6 feet wide and 2.5 feet depth means endpoints of the spotlight are at (3, 2.5) and (-3, 2.5)
now we can plug any point say (3,2.5) in above formula
3^2 = 4p(2.5)
9= 10p
P= 9/10= 0.9
Hence distance from the vertex to the focus is P=0.90 ft
so option D is correct.