(a) Given the parametric curve 41 : 7(0) = 0 i + sec j +2 tan k, (0,5), eliminate the parameter and sketch its graph. (b) Let S be the surface obtained by revolving C around the y-axis. Sketch the surface S and find a parametrization for S as a surface of revolution. (c) Eliminate the parameters in (b) and find an implicit equation for the surface of revolution S. 2 1 (d) Show that the point A (1, lies on the surface S and use the grid curves of V3' 3 the parametrization in (b) to find parametric equations for the tangent plane to S at A. (e) Use the implicit equation in (c) to find an implicit equation for the tangent plane to the surface at A. (f) Explicitly show that your answers in (d) and (e) are compatible. (g) Find the point(s) on the surface whose tangent plane is parallel to the plane x+3y+z = 1. (a) Given the parametric curve 41 : 7(0) = 0 i + sec j +2 tan k, (0,5), eliminate the parameter and sketch its graph. (b) Let S be the surface obtained by revolving C around the y-axis. Sketch the surface S and find a parametrization for S as a surface of revolution. (c) Eliminate the parameters in (b) and find an implicit equation for the surface of revolution S. 2 1 (d) Show that the point A (1, lies on the surface S and use the grid curves of V3' 3 the parametrization in (b) to find parametric equations for the tangent plane to S at A. (e) Use the implicit equation in (c) to find an implicit equation for the tangent plane to the surface at A. (f) Explicitly show that your answers in (d) and (e) are compatible. (g) Find the point(s) on the surface whose tangent plane is parallel to the plane x+3y+z = 1