### Millennium Hotel St. Louis Outdoor Pool Math Projects

P10 (-183.1437, 42.25752) P23 (-243.6437, 42.25752)

P31 (-213.1437, 42.25752) P32 (-153.1437, 42.25752)

P34 (-251.1437, 42.25752) P33 (-236.1437, 42.25752)

The Millennium Hotel has two outdoor swimming pools that were on the original blueprints as an ellipse and a circle.

The equations for the ellipse are:

* y = 0.618034 (900 - (x + 183.1437)^2)^0.5 + 42.25752*

and

* y = -0.618034 (900 - (x + 183.1437)^2)^0.5 + 42.25752*
Find the foci.

Find the length of the major and minor axes.

Write the equation of this ellipse in the standard form:

* (x - h)^2/a^2 + (y - k)^2/b^2 = 1*
Are the pools located in the correct position on the coordinate graph?

How would you change their locations if your answer is no?

Find the equation of the circle for the circular pool.

Find the surface area of each pool.

With thanks to college algebra students: Chip Fournier, Jeremy Freeman, Joseph Koepke, Nathan Remer and Joshua Tadrick for their Regal Riverfront Hotel graphs and calculations particularly those of the pools.

A "Service Learning" Project to provide web pages for our community's better understanding of mathematics.

Millennium Hotel Math Projects

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