Let M be a surface in R oriented by a unit normal vector fieldU = g?U? + g?U? +g?U?Then the Gauss map G: M->? of

Let M be a surface in R² oriented by a unit normal vector fieldU = g?U? + g?U? +g?U?Then the Gauss map G: M->? of M sends each point p of M to the point (g?(p), g?(p), g?(p)) of the unit sphere ?. For each of the following surfaces, describe G(M) of the Gauss map in the sphere ?:(a) Cylinder, x² + y² = r²(b) Cone, z = ?(x² + y²)(c) Plane, x+y+z=0(d) Sphere, (x - 1)² + y² + (x + 2)² = 1This is a Differential Geometry problem.