# Parameterize the intersection of the surfaces (x+2)^2 + (y-5)^2 = 36, -2x + y + 3z = 1

## Question:

Parameterize the intersection of the surfaces {eq}(x+2)^2 + (y-5)^2 = 36, \\ -2x + y + 3z = 1 {/eq}

## Parametric Curves:

We have the intersection of a cylindrical surface and a plane, which gives us a circle, an ellipse or lines. To parameterize the curve of intersection we use cylindrical coordinates.

We parametrize the cylindrical surface by using polar coordinates for its base which is a circle centered at (-2, 5) and has radius 6. This gives us...

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