A railroad tunnel is shaped like a semiellipse as shown below. The height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

Question

anonymous · Answer

attachment

zehanz · Answer

Unfortunately, the picture doesn't look much like a semiellipse, because the points that are on the x-axis do not have a vertical tangent line.

Ignoring this, the "ellipse" goes through (0, 58) and (0, -58) and (21, 29).

The general formula is: $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$.

(0, 58) means: x=0 and y=58. Put these in the equation. You can caclulate b.

Once you've got b, put (21, 29) in the equation. Then you can calculate a.

anonymous · Answer

Ok, is this correct?

x^2/588 + y^2/3364 = 1

anonymous · Answer

@ZeHanz

zehanz · Answer

Hold on, let me do it myself :)

anonymous · Answer

Ok, thanks :)

zehanz · Answer

I got the same, so it must be true :D

anonymous · Answer

Great, thanks so much for your help! :)

zehanz · Answer

YW!