John is planning to build an arched trellis for the entrance to his botanical garden. The arch is to be in the shape of the upper half of an ellipse that is 4 feet wide at the base and 7 feet high.

Question

Find the equation for the ellipse when a rectangular coordinate system is positioned with the origin at the center of the ellipse.

Answer 1

you have semi-axes of 2 and 7/2, with the longer axis vertical. So,

x^2/2^2 + y^2/(7/2)^2 = 1
or
x^2/4 + 4y^2/49 = 1