# 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.

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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