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.

A parabola is simply an approximately U-shaped curve which is mirror-symmetrical

The equation of the parabola is:

The equation of a parabola is represented as:

The parabola passes through:

--- the height

--- the width

Substitute in

Rewrite as:

Substitute 50 for c in

Substitute in

Add the above equations

Rewrite as:

Divide both sides by 4050

Substitute in

Divide both sides by 45

Substitute values a, b and c in

Hence, the equation of the parabola is:

Read more about parabolas at:

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Step-by-step explanation:

The parabola in Cartesian terms goes through the points:  

(0, 50) [assuming center at 0]

(-45,0) and (45,0) (touches floor at both edges)

Since it is round

So, width = 90 cm = Diameter

So, Radius =

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

Equation :  --A

since x= 0 gives 50  

So,

So,c = 50  

Since x= -45 and x = 45 gives the same result So, b has no effect i.e. b = 0

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

Now substitute values of a,b and c in A

Hence the equation of parabola is