Below are three True and False questions. Could you please teach me how to solve them by using the method of trace? Thank you very much.

question 1

The graph of the equation x^2 = 2z^2 + 3y^2 is an elliptic cone opening in the z direction.

The answer is false.

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.

Then answer is true

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.