SOLUTION: The light bulb of a parabolic reflector is placed at the focus of the reflector for better reflection. Suppose that the reflector is 18 inches and 10 inches deep. What is the equat

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Question 1143861: The light bulb of a parabolic reflector is placed at the focus of the reflector for better reflection. Suppose that the reflector is 18 inches and 10 inches deep. What is the equation of the parabola in the parabolic reflector?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The light bulb of a parabolic reflector is placed at the focus of the reflector for better reflection. Suppose that the reflector is 18 inches and 10 inches deep. What is the equation of the parabola in the parabolic reflector?
------------------
If you mean it's 18" wide:
If the parabola is symmetric about the y-axis and intersects the x-axis at (-9,0) and (9,0), then a 3rd point is (0,-10)
====================================
Use y = ax^2 + bx + c
-----
For (-9,0):
0 = 81a - 9b + c
---
For (9,0):
0 = 81a + 9b + c
0 = 81a - 9b + c
-------------------- Subtract
0 = 18b
b = 0
===============
For (0,-10)
-10 = 0a + 0b + c
c = -10
-----
For (9,0):
0 = 81a -10
a = 10/81
===========================
A parabola is
=============
Note that this is A parabola, not THE parabola. It can be moved and rotated which would give different equations.


Answer by ikleyn(52804)   (Show Source): You can put this solution on YOUR website!
.

In this problem the words related to the light bulb and to the focus are all  IRRELEVANT.

The correct formulation after editing,  removing all unnecessary words,  is THIS : 


    A parabolic reflector has the opening of 18 inches in diameter and is 10 inches deep. 
    What is an equation of the parabola in the parabolic reflector?


The rest of the words in the original formulation are only to make an obstacle for a reader
to quick and correct understanding the problem.



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