SOLUTION: The cross section of a flashlight is a parabola. The bulb is at the focus. Suppose the bulb is located 1/4 in from the vertex of the reflector. The width of the cross section throu

Algebra ->  Finance -> SOLUTION: The cross section of a flashlight is a parabola. The bulb is at the focus. Suppose the bulb is located 1/4 in from the vertex of the reflector. The width of the cross section throu      Log On


   

Question 991228: The cross section of a flashlight is a parabola. The bulb is at the focus. Suppose the bulb is located 1/4 in from the vertex of the reflector. The width of the cross section through the bulb is 2 in. What is an equation for this parabola?
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Try like this:
y=ax%5E2 for vertex at the origin. A point on the parabola reflector is (1,1/4) using your second part of the description. That is 1 inch on each "side" in the cross section at the bulb. That makes the two inch cross section.

1%2F4=a%2A1%5E2
a=1%2F4
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y=%281%2F4%29x%5E2, but this may not match the first part of the description for the bulb at the focus, 1%2F4 inch from the vertex. Recheck your problem description to be sure.