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.

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) (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
(-45,0) and (45,0) (touches floor at both edges,
it is round and diameter is (then radius is )

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

since gives

since and gives the same result it seems that has no effect; so,

plugging in and for the value for the expression

subtract from both sides and evaluate

divide both sides by

removing common factor of from top and bottom

so:

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