Parabola Question

best1230

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Mar 20, 2012
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Hi, I've been attempting this problem for a while now, but I just can't seem to work it out.

A spotlight has parabolic cross sections.
a) Write an equation for a cross section of the spotlight if the bulb is 15 centimeters from the vertex and the vertex is placed at the origin.
I was able to figure this part out: y=(1/60)x^2
b) If the spotlight has a diameter of 72 centimeters at its opening, find the depth of the spotlight if the bulb is 15 centimeters from the vertex.
I know the answer is supposed to be 21.6 cm, but I'm not quite sure how to arrive at it. I'm also not sure what is meant by "its opening".

Could anyone suggest a method to solve the problem? Thanks for your help!
 
Last edited:
1) Why do we need to be reminded that the bulb is 15 cm from the vertex? Very odd problem statement.

2) Opening is 72 cm. It's summetrical about the y-axis. This should suggest 36 cm on either side. Assuming \(\displaystyle y = \frac{1}{60}x^{2}\) is correct, solve for positive y, \(\displaystyle y = \frac{1}{60}(36\;cm)^{2}\) You wrote the equation to help you. Why not use it?
 
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