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Question 35074This question is from textbook
: could you help me solve a headlight mirror concerning parabola's.
a car headlight mirror has a parabolic cross section with diameter 6in. and depth 1 in.
A) position a coordinate system with the origin at the vertec and x-axis on the parabola's axis of symmetry and find an equation of the parabola
b) how far from the vertex should the bulb be positioned if it is to be placed at hte focus
This question is from textbook
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! could you help me solve a headlight mirror concerning parabola's.
a car headlight mirror has a parabolic cross section with diameter 6in. and depth 1 in.
A) position a coordinate system with the origin at the vertec and x-axis on the parabola's axis of symmetry and find an equation of the parabola
LET O BE THE ORIGIN AND VERTEX,F THE FOCUS,OF IS X AXIS...
EQN. OF PARABOLA IS
Y^2=4AX...WE HAVE DIAMETER OF MIRROR AS 6" AT A DEPTH OF 1"FROM VERTEX/ORIGIN
SO (1,6/2) AND (1,-6/2) ARE POINTS ON THE PARABOLA..SO
6^2=4A*1
4A=36
A=9
HENCE EQN . OF PARABOLIC MIRROR IS Y^2=36X
b) how far from the vertex should the bulb be positioned if it is to be placed at hte focus
BULB IS TO BE AT FOCUS.FOCUS IS AT (A,0)..SO WE SHOULD PLACE IT A"=9" FROM VERTEX
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