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The original Ferris wheel was built in 1893 by Pittsburgh, Pennsylvania,
bridge builder George W. Ferris. The Ferris wheel was originally built
for the 1893 World’s Fair in Chicago, but was also later reconstructed
for the 1904 World’s Fair in St. Louis. It had a maximum height of 264 feet
and a wheel diameter of 250 feet. Find an equation for the wheel
if the center of the wheel is on the y-axis.
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The height of the center is = 264 - 125 = 139 ft over the ground.
So, the center coordinates are x = 0, y = 139 ft.
The radius is 250/2 = 125 ft.
The standard equation of the wheel in this coordinate system is
+ = 125^2.
Solved.
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Comment from student: Thank you for your time. Tell me, what would be the general equation of the circle in this case?
My response: I provided the standard form equation of the circle.
The problem does not say explicitly, which form equation is requested,
so my answer is just enough.
If you want the general form equation, open parentheses and make FOIL.
It is just elementary technical job.
A person, who obtained such problem to solve, should have the necessary
technique at the tips of his/her fingers (like a pianist) to do this step AUTOMATICALLY
without asking any questions.
If you can not do it automatically on your own, then you need to return back
in 3 - 4 - 5 grades/classes in your studies.