I know how to do part 1 and 2 , but then i dont know how to do part 3. Can you please help. Here is the problem

Given the surface : x2 + y2 + 3z2 = 4.

1. Find a normal vector and the tangent plane to this surface at the point ( 0.6, 0.8, 1.0 ).

2. Is there a point on this surface at which the tangent plane is parallel to the plane 8x + 6y + 30z = 1 ? If so, find the point. If not, explain why not.

3. Does the tangent plane from part 1) give the linear approximation for some function f (x, y) of two variables at the point ( 0.6, 0.8, 1.0 ) ?

If so, find the function f (x, y) and its linear approximation at the point given point and explain how the gradient vector f is related to the normal vector from part 1).