1. ## graphing quadratic surfaces by the method of trace

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.

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.

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.

2. Originally Posted by Jenny20
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.

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

Yes, $z$ has a constant value.