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Question 534336: An electric heater is being designed as a parabolic reflector 6'' deep. To prevent accidental burns, the center of the heating element is placed at the focus, which is set at 1.5'' from the vertex of the reflector.
A) Find the equation that describes the shape of the reflection
B) How wide is the reflector
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! An electric heater is being designed as a parabolic reflector 6'' deep. To prevent accidental burns, the center of the heating element is placed at the focus, which is set at 1.5'' from the vertex of the reflector.
A) Find the equation that describes the shape of the reflection
B) How wide is the reflector
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Visualize a parabola with its vertex at the origin or (0,0) and it opens upwards.
Standard form of an equation for this parabola: (x-h)^2=4p(y-k), (h,k) being the (x,y) coordinates of the vertex.
A) Since the vertex is placed at the origin, the equation becomes x^2=4py
p is the distance from the vertex to the focus on the axis of symmetry=1.5"
equation now becomes x^2=6y
B) Since the parabolic reflector is 6" deep the edge is a point on the equation where y=6.
x^2=6*6=36
x=±√36=±6
So reflector is 12 inches wide
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