#5, (a) Classify and sketch the surface x+y²+z² = 4, (b) Find the tangent plane at the point (2,-1,1). Find parametric equations for the normal line at (2,-1,1),

Find parametric equations and a parameter interval for the motion of a particle that starts at the point (-2, 0) in the xy-plane and traces the circle x2 + y2 = 4 three times clockwise.

Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the surface z = x²y and (a) the plane x = 1 (b) the plane y = 3.

Let L be the line that passes through the points (3,4,5) and (7,−1,2). (a) Write parametric equations for theL. (b)  Find the point at whichLcrosses through the planex+z= 10. (c)  Find an equation for the plane through (7,−1,2) perpendicular to the lineL.

Sketch the plane curve represented by the given parametric equations x = t2 + t + 1, y = 2t. Then use interval notation to give relation’s domain and range.

Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x −4y + 2z = 0and 2x + 3y −z +1 = 0.