SOLUTION: In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 50 centimeters tall and 90 centimeters wide. Find the equation of the parabola.

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Question 419369: In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 50 centimeters tall and 90 centimeters wide. Find the equation of the parabola.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


the parabola in Cartesian terms goes through the points:

(0, 50).... assume mirror is face down and center at 0
(-45,0) and (45,0) (touches floor at both edges,
it is round and diameter is 90 (then radius is 45)

take points (0, 50) and (45,0) and (-45,0)

y+=+ax%5E2+%2B+bx+%2B+c
since x=+0 gives 50
c+=+50
since x=+-45 and x+=+45 gives the same result it seems that b has no effect; so,
b+=+0

plugging in b and c for the value 45 for the expression

a%2A45%5E2+%2B0%2A45+%2B+50+=+0
subtract 50 from both sides and evaluate
a45%2A+45+=+-50
2025a=-50

divide both sides by 2025
a+=+-50%2F2025
removing common factor of 25 from top and bottom
a+=+-2%2F81
so:
y+=+-%282%2F81%29x%5E2+%2B+50