Question

A railroad tunnel is shaped like a semi ellipse as shown below. The height of the tunnel at the center is 27 ft and the vertical clearance must be 9 ft at a point 24 ft from the center. Find an equation for the ellipse.

Answer 1

the equation of the ellipse is y^2/a^2 + x^2/b^2 = 1

We also know that the maximum y value is 27, so
y^2 / 729+ x^2/b^2 = 1


Now it's just a matter of finding b.
In order to do so, just plug in the x and y values you're given

Answer 2

9^2/729 + 24^2/b^2 = 1
? - ?/729 = 24^2/b^2
solve b and the ?-? from here and you have your ellipse.
hope this helps

Answer 3

I got 81/729+576/b^2=1

Answer 4

@jslp3z

Answer 5

So 81/729=576/b^2?

Answer 6

i believe that is correct !