Question 1207915
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In 2008, the Singapore Flyer opened as the world’s largest Ferris wheel. 
It has a maximum height of 165 meters and a diameter of 150 meters, 
with one full rotation taking approximately 30 minutes. 
Find an equation for the wheel if the center of the wheel is on the y-axis.
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<pre>
The radius of the wheel is half of its diameter, i.e. 150/2 = 75 meters.

The center of the wheel is  at the height of 165-75 = 90 meters over the ground.


The problem does not tells, which coordinate system to use; so, I will chose
the system at the ground level.


In this system, the center of the wheel is the point with coordinates (0,90) meters.


So, in standard equation of a circle

    {{{(x-x[0])^2}}} + {{{(y-y[0])^2}}} = r^2,


where  ({{{x[0]}}},{{{y[0]}}})  is the center,  "r"  is the radius, we should take

    {{{x[0]}}} = 0,  {{{y[0]}}} = 90,  r = 75.


Thus, the equation of this wheel is

    {{{x^2}}} + {{{(y-90)^2}}} = {{{75^2}}},

or

    {{{x^2}}} + {{{(y-90)^2}}} = 5625.
</pre>

Solved.


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In this problem, the information about the rate of rotation 
(the duration of one rotation) is irrelevant to the question.


A TWIN problem was solved at this forum yesterday under this link


https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1207910.html