# Intersection of surfaces

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?

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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.