SOLUTION: An arch is semi-elliptical with a base that is 20 feet wide and a height at the center of 8 feet. How high is the arch 6 feet from the center of the base?

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Question 76472: An arch is semi-elliptical with a base that is 20 feet wide and a height at the center of 8 feet. How high is the arch 6 feet from the center of the base?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
If you picture the arch with the base sitting on the x-axis and centered on the y-axis, it is an ellipse with a major axis of 20 and a minor axis of 16 centered at the origin (0,0)

the equation of this ellipse is %28x%5E2%29%2F10%5E2%2B%28y%5E2%29%2F8%5E2=1...or 16x%5E2%2B25y%5E2=1600

at x=6 (or -6) the equation is 576%2B25y%5E2=1600...or 25y%5E2=1024...or 5y=32...so y=6.4 and height is 6.4 feet