SOLUTION: The opening of the a cave 20 feet wide is in the shape of semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The opening of the a cave 20 feet wide is in the shape of semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?      Log On


   



Question 1019412: The opening of the a cave 20 feet wide is in the shape of semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Making the center of floor entrance correspond to the origin (0,0), the semi-ellipse would follow the equation
x%5E2%2F%2820%2F2%29%5E2+%2B+y%5E2%2F15%5E2+=+x%5E2%2F100%2By%5E2%2F225+=+1
5 feet from the center, x = 5, and after substitution gives
25%2F100+%2B+y%5E2%2F225+=+1
==> y%5E2%2F225+=+3%2F4
<==> y%5E2+=+%283%2F4%29%2A225
==> y+=+%28sqrt%283%29%2A15%29%2F2 after taking the positive square root.
y = 12.99 feet, or 13 feet approximately.