   Chapter 12.6, Problem 52E

Chapter
Section
Textbook Problem

# Show that the curve of intersection of the surfaces x2 + 2y2 − z2 + 3x = 1 and 2x2 + 4y2 − 2z2 − 5y = 0 lies in a plane.

To determine

To show: The curve of intersection of surfaces lies in a plane.

Explanation

Given data:

Surfaces x2+2y2z2+3x=1 and 2x2+4y22z25y=0 .

Consider the given surface equations.

x2+2y2z2+3x=1 (1)

2x2+4y22z25y=0 (2)

Multiply equation (2) by 2.

2x2+4y22z2+6x=2 (3)

Subtract equations (3) and (2).

2x2+4y22z2+6x(2x2+4y22z25y

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