Find the Eccentricity E of the Ellipse $30 \mathrm { ft }$

question 76

Multiple Choice

Find the eccentricity e of the ellipse.
-A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is $30 \mathrm { ft }$ and the vertical clearance must be $20 \mathrm { ft }$ at a point $5 \mathrm { ft }$ from the center. Find an equation for the ellipse.

• A) \(\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 900 } = 1\)
• B) \(\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 400 } = 1\)
• C) \(\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 45 } = 1\)
• D) \(\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 900 } = 1\)