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Question 327106: A spotlight has a parabolic cross section that is 8ft wide at the opening and 3.5 ft. depp at the vertex. how far from the vertex is the focus in feet?
Answer:
thank you for your time!
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! If I understood your question correctly as typed, the vertex should be at the origin or at the point (0,0). This parabola opens upward and so it has the form
x^2 = 4Py.
Let P = distance of vertex from focus
The parabola is 8 feet wide and 3.5 feet.
This means that the end points are (-4,3.5) and (4,3.5).
We use the point (4,3.5) which has a positive x-coordinate since we are dealing with distance and distance is a positive measure.
x^2 = 4Py
(4)^2 = 4P(3.5)
16 = 14P
16/14 = P
The focus is at the point (0,P), which is P units from the vertex's origin location (0,0).
The focus should be 16/14 feet or about 1.14 feet from the vertex.
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