Here's the question,
Determine level set L(f,c) for the following
f(x,y,z)= x2-2x+y2+z2-6y+11 ,c=5
As we have three variables, the level set is a level surface. It is given by the equation
As this is quadratic in x, y, and z, the result is a quadric.
(completing the square for x and y)
The resulting geometric surface should be easy to see (hint: remember the distance formula).