SOLUTION: A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep. How far from the vertex should the filament of the bulb be placed if

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep. How far from the vertex should the filament of the bulb be placed if      Log On


   

Question 814895: A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?
Answer by lwsshak3(11628) About Me  (Show Source):
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A parabolic reflector for a car headlight forms a bowl shape that is 6 in. wide at its opening and 3 in. deep. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?
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Draw a parabola that opens up with vertex at the origin.
basic equation for parabola:
x^2=4py
known point(3,3)(top right edge of the bowl)
3^2=4p3
4p=9/3=3
p=3/4
axis of symmetry:x=0
focus:(0,3/4)(p-distance above vertex on the axis of symmetry)
How far from the vertex should the filament of the bulb be placed? 3/4 inch