I am so confused with this problem.
"In a factory, a parabolic mirror to be be used in a searchlight was placed on the floor. It measured 50 cm tall and 80 cm wide. Find the equation of the parabola."

You can determine the equation of a parabola if you know three points. For this problem if you define the origin as the point where the parabolic mirror touches the floor, then the three points you know are:

0,0
40,50
-40,50

Now you should be able to use these data points in the general equation for a parabola:


y-y_0 = A(x-x_0)^2


Where A, y0, and x0 are unknown constants.