How do you find the equation of a circle?

The equation of a circle is given in the form (x-a)² + (y-b)² = r², in which the centre of the circle is (a,b) and the radius of the circle is 'r'. If you can figure out or are given the co-ordinates of the centre of the circle and the radius then these values can be plugged into the above equation to find the answer. Occasionally, you may not be given these values and will instead be given the equation in the form x²+y²+cx+dx=k, in which c, d and k are constants. In this case, you can "complete the square" for x and y in order to rearrange the equation into the model above. This will allow you to then also figure out the centre of the circle and the radius should you need it.