A circle with centre C has equation x^2 + y^2 + 2x - 6y - 40 = 0. Express as (x - a)^2 + (y - b)^2 = d.
First we must complete the square on both x and y. To complete a square we must take the number before the x and half it, for example nx we get n/2. We then write it as (x + n/2)2 - (n/2)2.
So for our question we have 2x so we will write (x + 1)2 - (1)2. Then we repeat for y. We have -6y so we will write (y - 3)2 - (3)2.
We then write all of this together as (x + 1)2 - 1 + (y - 3)2 - 9 - 40 = 0. Rearrange and we get (x + 1)2 + (y - 3)2 = 50
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