Please show detailed work. Thank you.

Let S be the surface given by the cartesian equation

{a} There are two ways we can visualize this surface. First, since we can isolate the variable 11:}, we can think of .5' as the graph of the function ff. . = 1111.1 + 'Efl + all}- The vector V. P} in this case represents the direction in the ; plane for which the corresponding path on the surface 5' at the point I) sees the largest increase in the .:1r:-direction. Sketch the surface 5', mark the point P [:1 _ ll], 1:} and draw the path on .5' in the direction of V P}. (b) Now, let's think ofS as the zero set of the function As we saw in class, a normal vectorto 5' at the point 1' is given by V 'l}. Use this to nd the cartesian equation for the tangent plane to .5' at the point P [:111{ 2 1:}