# Whether the equation x 2 y 2 + x y = 1 is symmetric about x-axis or y-axis or origin.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.8, Problem 79E
To determine

## To calculate:Whether the equation x2y2+xy=1 is symmetric about x-axis or y-axis or origin.

Expert Solution

The equation x2y2+xy=1 is symmetric only with respect to origin.

### Explanation of Solution

Given information:

The equation x2y2+xy=1 .

Formula used:

The function is symmetric about the x-axis, when y is replaced by y , the equation remains unchanged.

The function is symmetric about the y-axis, when x is replaced by x , the equation remains unchanged.

The function is symmetric with respect to origin, when y is replaced by y and x is replaced by x , the equation remains unchanged.

Calculation:

It is provided that the equation is x2y2+xy=1 . Construct a table to evaluate the value of y for different values of x.

Recall that the function is symmetric about the x-axis, when y is replaced by y , the equation remains unchanged.

Replace y by y in the equation x2y2+xy=1 ,

x2(y)2+x(y)=1x2y2xy=1

The equation is changed. Therefore, the equation x2y2+xy=1 is not symmetricabout the x-axis.

Recall that the function is symmetric about the y-axis, when x is replaced by x , the equation remains unchanged.

Replace x by x in the equation x2y2+xy=1 ,

(x)2y2+(x)y=1x2y2xy=1

The equation is changed. Therefore, the equation x2y2+xy=1 is not symmetricabout the y-axis.

Recall that the function is symmetric with respect to origin, when y is replaced by y and x is replaced by x , the equation remains unchanged.

Replace x by x and y by y in the equation x2y2+xy=1 ,

(x)2y2+(x)(y)=1x2y2+xy=1

The equation is unchanged. Therefore, the equation x2y2+xy=1 is symmetricabout the origin.

Thus, the equation is symmetric only about origin.

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