7. (3) Sketch the top half of the sphere 12 +3;2 + 2:3 = 5. Check that P = (1, 1I J5) is on this sphere and add this point to your picture. (b) Find a function f{z,y) whose graph is the top-half of the sphere. Hint: solve for z. (c) Imagine an ant walking along the surface of the sphere. It walks down the sphere along the path C that passes through the point P in the direction parallel to the yz-plane. Draw this path in your picture. (d) Find a. parametrization r{t) of the ant's path along the portion of the sphere shown in your picture. Specify the domain for r, i.e. the initial time when the nut is at P and the nal time when it hits the :typlune