Find a parametric equation of the curve of intersection of

Question

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 e^t) i + (3 cos e^t) j.

(b) r = -2i + tj + (t² - 1) k.

Attachment:- multivariable-calculus.pdf