Question

An arch has the shape of a semi ellipse that is 10 ft. long and 3 ft. high at the center. How high is the arch at a point 2 ft. from the center? *

Answer 1

We are told that 2a = 10 and 2b = 3
so the equation of the ellipse is
x^2/25 + y^2/2.25 = 1 , using x^2/a^2 + y^2/b^2 = 1

so when x = 2
4/25 + y^2/2.25 = 1
y^2/2.25 = 21/25
y^2 = 2.23(21/25) = 1.89
y = √1.89 = 1.375 ft

Answer 2

we have a = 5, b = 3
x^2/25 + y^2/9 = 1
now find y when x = 2

Answer 3

Agree with oobleck.
I read the height to be the whole ellipse not the semi.