x^2 + y^2 - 6x + 8y = 11
It should end up being a circle or ellipse.
x^2 - 6x + y^2 + 8y = 11
We want to make (x - 3)^2, but that has to have a +9 on the end, so we do this:
x^2 - 6x + 9 - 9 + y^2 + 8y = 11
(x - 3)^2 - 9 + y^2 + 8y = 11
Now we want to make (y + 4)^2, but that has to have a +16 on the end, so we do this:
(x - 3)^2 - 9 + y^2 + 8y + 16 - 16 = 11
(x - 3)^2 - 9 + (y + 4)^2 - 16 = 11
(x - 3)^2 + (y + 4)^2 - 25 = 11
(x - 3)^2 + (y + 4)^2 = 36
(x - 3)^2 + (y + 4)^2 = 6^2
Equation of a circle: (x - a)^2 + (y - b)^2 = r2
Circle centered at (a,b) with radius r.
It's a circle centered at the point (3,-4) with a radius of 6.