2. Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces S₁: x²+y² + z² = 30 and S2: z = x² + y² at the point (1,2,5).

Determine the points of intersection of the line with parametric equations L: x= 2t + 7 , y= 3t - 1, tER, with the circle x² + y²= 41

2. Let C be the parametric curve X = 2 sint + 1 y = 2 cost where t E R. (a) By eliminating t, derive an equation relating and y. (b) Sketch the graph of C on the xy-plane. Indicate the direction as t increases on the graph.

Find the parametric equation of the line segment from A(1,2,3) to B(5.0, 1), where for t = 0 you are at point A and for t= 1 at point B..