A ferris wheel has a maximum height of 230 feet and a wheel

A ferris wheel has a maximum height of 230 feet and a wheel diameter of 210 feet. Find an equation for the wheel if the center of the wheel is on the y-axis and y represents the height above the ground.

Solution

diameter = 210 feet

so, radius = 210 / 2 = 105 feet

standard equation of wheel (circle ) is given by

(x-h)^2 + (y-k)^2 = r^2

maximum height = 230 feet and diameter = 210 feet

which means wheel is 230 - 210 = 20 feet off the ground

center = 20 + radius = 20 + 105 = (0,125) feet

equation of wheel is

(x-h)^2 + (y-k)^2 = r^2

x^2 + (y-125)^2 = 105^2