SOLUTION: 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 f

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.

RELATED QUESTIONS
A field microphone has a parabolic cross section. It is 20 in wide at the opening and its (answered by lwsshak3)

A satellite dish has a parabolic cross section and is 6 ft deep. The focus is 4 ft from... (answered by lwsshak3)

A field microphone used at a soccer game has a parabolic cross section and is 26 in. wide (answered by josgarithmetic)

A field microphone used at a soccer game has a parabolic cross section and is 24 inches... (answered by lwsshak3)

A SEARCHLIGHT HAS A PARABOLIC REFLECTOR (HAS A CROSS SECTION THAT FORMS A BOWL) THE... (answered by Alan3354)

A SEARCHLIGHT HAS A PARABOLIC REFLECTOR (HAS A CROSS SECTION THAT FORMS A BOWL) THE... (answered by josgarithmetic)

A reflector for a satellite dish is parabolic in cross section, with the receiver at the... (answered by lwsshak3)

A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its... (answered by lwsshak3)