A Railroad Tunnel Is Shaped Like a Semi-Ellipse $\frac { x ^ { 2 } } { 300 } + \frac { y ^ { 2 } } { 100 } = 1$

Multiple Choice

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 20 ft and the vertical clearance must be 10 ft at a point 15 ft from the center. Find an equation for the ellipse.

A) $\frac { x ^ { 2 } } { 300 } + \frac { y ^ { 2 } } { 100 } = 1$
B) $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 400 } = 1$
C) $\frac { x ^ { 2 } } { 300 } + \frac { y ^ { 2 } } { 400 } = 1$
D) $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 300 } = 1$