How do you find the equation of the circle given center at (1,-3), and radius 10?
Suppose the centre of the circle was at the origin (where the x axis crosses the y axis). Then the equation would be:
The reason for this format is that the length of the radius (which is of fixed length) can be related to x and y by Pythagoras. However, the circle centre is not at the origin. It is at
So we can mathematically make this work by 'theoretically' moving the actual centre to a new centre located at the origin.
Thus we would have:
But the radius is 10 so we have