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?
+2666 Isolate the constant: \(x^2 + y^2 + 5x - 5y = 18\)
Rearrange as follows: \((x^2 + 5x) + (y^2 - 5y) = 18\)
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 \(r^2\), meaning the area of the circle, in terms of pi, is \(\color{brown}\boxed{{30.5 \pi}}\)
