Answered: Consider the surface defined by the…

Consider the surface defined by the equation 2.x2 – 2y2 – z = 0. (a) Choose any one of the variables and give it a fixed value. Then sketch the corre- sponding trace.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 21E

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Question

Consider the surface defined by the equation 2x2 - 2y?-z = 0.
(a) Choose any one of the variables and give it a fixed value. Then sketch the corre-
sponding trace.
you
know.
(b) Identify the surface. Very briefly explain how

Expert Solution

Step 1

The equation is the form $z = f (x, y)$ represents a surface in the space. In this problem the equation of the surface is $z = 2 x^{2} - 2 y^{2}$ . In the first part of the problem, we have to give a fixed value to one of the variables and then sketch the corresponding trace. In the second part, we have to identify the surface $z = 2 x^{2} - 2 y^{2}$ .

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