Circles

\(2x^2+2y^2+10x-6y-18=0\)

First, you want to put this equation in a form that you can get information about the circle from.

Rearrange a bit:

2x²+10x+2y²-6y=18

Factor

2(x²+10x)+2(y²-3y)=18

Divide by 2

(x²+10x)+(y²-3y)=9

Add numbers to turn into perfect squares, making sure to add the same to both sides

(x²+10x+25)+(y²-3y+2.25)=9+25+1.5

Factor

(x+5)²+(y-1.5)²=36.25

(-5,1.5) is the center and 36.25 is the radius squared, so 36.25pi is the area.

2x^2+2y^2+10x-6y-18=0

 

2x^2+10x+2y^2-6y=18

 

2(x^2+5x)+2(y^2-3y)=18

 

(x^2+5x)+(y^2-3y)=9

 

(x^2+5x+6.25)+(y^2-3y+2.25)=9+6.25+2.25

 

 

(x+2.5)^2+(y-1.5)^2=17.5

 

17.5pi?