# Whether the set of points ( 0 , − 2 ) , ( 1 , − 2 ) and ( 2 , − 2 ) lie on the graph of the equation x 2 + x y + y 2 = 4 . ### 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 51E
To determine

## To calculate: Whether the set of points (0,−2),(1,−2) and (2,−2) lie on the graph of the equation x2+xy+y2=4 .

Expert Solution

The points (0,2)and (2,2) lie on the graph of the equation whereas the point (1,2) does not lie on the graph.

### Explanation of Solution

Given information:

The set of points (0,2),(1,2) and (2,2) and equation of graph x2+xy+y2=4 .

Formula used:

The set of all points (x,y) in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Calculation:

Consider the providedset of points (0,2),(1,2) and (2,2) and equation of graph x2+xy+y2=4 .

Recall that the set of all points (x,y) in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Substitute the point (0,2) in the equation x2+xy+y2=4 and check whether left hand side is equal to right hand side.

02+0(2)+(2)2=44=4

The above equality holds true, the point (0,2) lie on the graph of the equation.

Substitute the point (1,2) in the equation x2+xy+y2=4 and check whether left hand side is equal to right hand side.

12+1(2)+(2)2=412+4=43=4

The above equality does not hold, the point (1,2) does not lie on the graph of the equation.

Substitute the point (2,2) in the equation x2+xy+y2=4 and check whether left hand side is equal to right hand side.

22+2(2)+(2)2=444+4=44=4

The above equality holds true so, the point (2,2) lie on the graph of the equation.

Thus, the points (0,2) and (2,2) lie on the graph of the equation whereas the point (1,2) does not lie on the graph.

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