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# Intersection of surfaces

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How do you find the equation of the curve of intersection of the surfaces
z = x^2 and x^2 + y^2 =1?

How can I show that the curve with parametric equations

x = sin t, y = cos t, z = sin^2 t

is the curve of intersection of these two surfaces?

https://brainmass.com/math/algebra/intersection-surfaces-449446

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

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The first surface is:
(1.1)
This is a cylinder aligned with the z-axis. Its cross section is a unit circle centered at the origin.

When we have a ...

#### Solution Summary

The intersection of surfaces are examined.

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