Solve the Problem $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 324 } = 1$

Solve the problem.
-A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 18 ft and the vertical clearance must be 12 ft at a point 5 ft from the center. Find an equation for the ellipse.

A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 324 } = 1$
B) $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 324 } = 1$
C) $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 144 } = 1$
D) $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 45 } = 1$

Correct Answer:

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