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

## Answer this Question

## Related Questions

- Trig - A railroad tunnel is shaped like a semiellipse as shown below. A ...
- Precalculus Trig (Geometry) - A rectangular doorway is 38 meters wide and 60 ...
- Circle geometry! - A circular tunnel, 20 m in diameter is blasted through a ...
- math - a tunnel under a river is 196.8 ft below the surface at its west point. ...
- Math - Question: A tunnel with a parabolic arch is 12 m wide. If the height of ...
- Physics - Planet Earth as a Spring. Assume that the Earth is perfect sphere of ...
- physics - Assume a planet is a uniform sphere of radius R that (somehow) has a ...
- Math - A tunnel under a river is 196.8 ft below the surface at its lower point. ...
- physics - a train goes into a tunnel at 20m/s and emerges from itat 55m/s. the ...
- Algebra 1 - William, a logistician, needs to route a freight train that is 20 ...