ellipse, Thank you!

Question

A certain bridge arch is in the shape of the top half of an ellipse 126 feet wide and 32 feet high. At what horizontal distance from the center of the arch is the height equal to 14.2 feet? Give your answer accurate to 2 decimal places.

 ___feet

Answer 1

Based on given information's, first you find equation of the ellipse. Since a=63 and b=32 equation of the ellipse is x^2/a^2 + y^2/b^2=1 or x^2/63^2+y^2/32^2=1.

Next, you have to find x such that y=14.2. Replacing y=14.2 into equation above and solving for x will give you horizontal distance from center of the arch to where height is 14.2 feet.

Hope this help.