A bridge is built in the shape of a semi-elliptical arch. The bridge has a span of 60 feet and a maximum height of 20 feet. Choose a suitable rectangular coordinate system and find the height of the arch at a distance of 10 feet from the center.
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x^2 / 30^2 + y^2 / 10^2 = 1
x = 10
10^2 / 30^2 + y^2 / 100 = 1
100/900 + y^2 / 100 = 1
1/9 + y^2 / 100 = 1
y^2 / 100 = 1 - 1/9
y^2 / 100 = 8/9
y^2 = 8 * 100 / 9
y = 2 * 10 * sqrt(2) / 3
y = 20 * sqrt(2) / 3
x = 10
10^2 / 30^2 + y^2 / 100 = 1
100/900 + y^2 / 100 = 1
1/9 + y^2 / 100 = 1
y^2 / 100 = 1 - 1/9
y^2 / 100 = 8/9
y^2 = 8 * 100 / 9
y = 2 * 10 * sqrt(2) / 3
y = 20 * sqrt(2) / 3