Find a parametrization of the intersection of the surfaces z = x^2 - y^2 and z = x^2 + xy - 6...

Question:

Find a parametrization of the intersection of the surfaces {eq}z = x^2 - y^2 {/eq} and {eq}z = x^2 + xy - 6 {/eq} using {eq}t = y {/eq} as a parameter.

The Curve of Intersection:

The intersection of two surfaces is the set of all the points in the space that satisfy the equations of both surfaces. We can find its parametric equations by solving these equations in terms of one chosen variable.

Answer and Explanation:

The curve of intersection satisfies the equations of both surfaces {eq}\displaystyle \; z = x^2 - y^2 \; \mbox{ and } \; z = x^2 + xy - 6 \; {/eq}....

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Graphs of Parametric Equations

from Precalculus: High School

Chapter 24 / Lesson 5
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