quiz_04D - -1 2 . Therefore, the shadow of the curve in the...

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Math 213 — Quiz 4 Name Solution 1. Find a vector function that represents the intersection of the cone z = p x 2 + y 2 and the plane z = 1 + y . The shadow of the curve in the xy -plane can be described by the equation p x 2 + y 2 = 1 + y , or x 2 + y 2 = (1 + y ) 2 = 1 + 2 y + y 2 . We may solve for y in this last equation to obtain y = x 2
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Unformatted text preview: -1 2 . Therefore, the shadow of the curve in the xy-plane can be parametrized by x = t, y = t 2-1 2 . We then nd that z = 1 + y = t 2 + 1 2 . So the curve is parametrized by the vector function r ( t ) = t i + t 2-1 2 j + t 2 + 1 2 k ....
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