Question

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 1

Y=-2/81x^2+50 is the answer 

Answer 2

Answer:

$y = \frac{-2}{81}x^2 + 50$

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 = $\frac{Diameter}{2}=\frac{90}{2} = 45 cm$

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

Equation :$y = ax^2 + bx + c$  --A

since x= 0 gives 50  

So, $50 = a(0)^2 + b(0) + c$

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  

$a\times 45^2 +0 \times 45 + 50 = 0$

$2025a = -50$

$a =\frac{ -50}{2025}$

$a =\frac{ -2}{81}$

Now substitute values of a,b and c in A

$y = \frac{-2}{81}x^2 + 50$

Hence the equation of parabola is    $y = \frac{-2}{81}x^2 + 50$