Let s be the surface with parametrization (x, y, z) = r(u, v) = u cos v i + u sin v j + u k u ≥ 0, 0 ≤ v ≤ 2π. (a) show that s is a cone. hint: find an equation of the form f(x, y, z) = 0 for this surface by eliminating u and v from the equations for x, y, and z above. (b) sketch the cone, together with the "grid" curves on the cone where (a) u = 2 and (b) v = π/4. (c) find a parametrization of the tangent plane to the cone at the point where (u, v) = (2, π/4). add this tangent plane to your sketch.