Question

A “sunburst” window above a doorway is
constructed in the shape of the top half of an ellipse, as
shown in the figure. The window is 20 in. tall at its highest
point and 80 in. wide at the bottom. Find the height of the
window 25 in. from the center of the base

Answer 1

The equation of an ellipse in standard from is
x^2 / a^2 + y^2 / b^2 = 1

from your description, a = 40, and b = 20
so we have
x^2 / 1600 + y^2 / 400 = 1
or : x^2 + 4y^2 = 1600

so when x = 25 ,
625 + 4y^2 = 1600
4y^2 = 975
y^2 = 243.75
x = appr 15.6 inches