Correct. An elliptic cone openning in the "x" direction.

Correct, it is true.question 2

The graph of (z-1) = [((x-2)^2)/7 + ((y-3)^2)/10] is an elliptic paraboloid with base at the point (2,3,1) and opening in the z direction.

Yes, has a constant value.question 3

If S is the surface determined by the euqation (x^2/4 ) +(y^2/9) +(z^2/16) =1 , then any trace of S which has more than one point and lies in a plane parallel to a coordinate plane is an ellipse.

The answer is true.

Thus, you get an ellipse.