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

question 185

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) \(\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 300 } = 1\)

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