In terms of pi, what is the area of the circle defined by the equation 2x^2+2y^2+10x-6y-18=x^2+y^2+5x-y?
Isolate the constant: x2+y2+5x−5y=18
Rearrange as follows: (x2+5x)+(y2−5y)=18
Add 6.25 to complete the square on x, and add another 6.25 to complete the square on y.
This gives: (x+2.5)2+(y−2.5)2=30.5.
Note that the constant (30.5) is r2, meaning the area of the circle, in terms of pi, is 30.5π