Let the center of the ellipse be at (0,0). Then you have
a = 164/2 = 82
b = 52
so the equation is
x^2/82^2 + y^2/52^2 = 1
So now you just have to solve for p.
p^2/82^2 + 11^2/52^2 = 1
The arch of the bridge below is an ellipse, a semi-ellipse"As shown in the figure below, the arch is 164 m long and has a height of 52 m at the center. The height of the arch is 11 m at point p. Find the distance from p to the center. Round your answer to the nearest hundredth. Do not round any intermediate computations.
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