The Set of Points On $z = x ^ { 2 } - 3 x y + y ^ { 2 }$

Multiple Choice

The set of points on $z = x ^ { 2 } - 3 x y + y ^ { 2 }$ at which the tangent plane is parallel to the xy-plane is

A) $\{ ( 0,0,3 ) \}$
B) $\{ ( 0,0,2 ) \}$
C) $\{ ( 0,0,1 ) \}$
D) $\{ ( 0,0,0 ) \}$
E) $\{ ( 0,0,5 ) \}$