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Find a parametric equation of the curve

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Reference no: EM13295207

1. Name and sketch the surface: z = 4x2+ y2+ 8x - 2y

2. (a) Find a parametric equation of the curve of intersection of the paraboloid z = 3 x2 - y2 and the plane z = 2y.

(b) Find an equation of the orthogonal projection of this curve to the xy-plane.

3. The curves below are given by their vector equations. Describe them in Cartesian coordinates. What are their geometric names?

(a) r = 3 sin et) i + (3 cos et) j.

(b) r = -2i + tj + (t2 - 1) k.


Attachment:- multivariable-calculus.pdf

Reference no: EM13295207

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