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

question 198

Multiple Choice

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) \(\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 45 } = 1\)

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