Posted by **Stacey grahaM** on Sunday, May 2, 2010 at 4:53pm.

A railroad tunnel is shaped like semi-ellipse. The height of the tunnel at the center is 69 ft and the vertical clearance must be 23 ft at a point 16ft from the center. Find an equation for the ellipse.

- Trig -
**Reiny**, Sunday, May 2, 2010 at 5:20pm
b = 69, a is unknown, and the point (16,23) is on it

let the equation be

x^2/a^2 + y^2/69^2 = 1

16^2/a^2 + 23^2/69^2 = 1

256/a^2 = 1 - 529/4761

256/a^2 = 8/9

8a^2 = 2304

a^2 = 288

x^2/288 + y^2/4761 = 1

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