# The x- and y- intercepts for the equation x 2 + y 3 − x 2 y 2 = 64 and the graph of the equation is provided below,

BuyFind

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.8, Problem 56E
To determine

Expert Solution

## Answer to Problem 56E

The x-intercepts are 8 and 8andy-intercept is 4 .

### Explanation of Solution

Given information:

The equation x2+y3x2y2=64 and the graph of the equation is provided below,

Formula used:

The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.

Calculation:

Consider the provided equation x2+y3x2y2=64 and the graph of the equation is sketched below,

Observe from the graph that the curve intersects x-axis at two points 8 and 8 also y-axis at one point that is 4 .

Recall that the x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

Substitute y=0 in the equation x2+y3x2y2=64 ,

x2+03x2(0)2=64x2=64x=±8

Therefore, x-intercepts are 8 and 8.

Recall that the y-intercepts are the points on x-axis where the graph of the equation intersects the y-axis.

Substitute x=0 in the equation x2+y3x2y2=64 ,

02+y3(0)2y2=64y3=64y=4

Therefore, y-intercept is 4 .

Thus, the x-intercepts are 8 and 8andy-intercept is 4 .

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