Circle C has equation x^2 + y^2 - 6x + 4y = 12, what is the radius and centre of the circle
The equation of a circle is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the centre of the circle, and r is the radius. To condense our equation into this form we have to use the technique of completing the square, which says that you can write an equation of form x^2 + bx + c in the form (x + b/2)^2 - (b/2)^2 + c. Completing the square for the x terms leaves us with (x-3)^2 - 9, and for the y terms it leaves us with (y+2)^2 - 4, so the equation becomes (x-3)^2 + (y+2)^2 - 13 = 12, add 13 to both sides and we end up with an equation in the form of the circle equation, (x-3)^2 + (y+2)^2 = 25, telling us the centre of the circle is (3,-2) and the radius is 5
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