How do you find the equation of a circle given the coordinates of it's centre and a point on the circle?
You need to know the general equation for a circle always looks like: (x-a)2+(y-b)2=r2 where r is the radius of your circle, a is the x coordinate of the centre of your circle and b is the y coordinate of the centre of your circle. So when we are given the coordinates of the centre of a circle we immediately know what a and b are. For example, if the question states that the circle has centre (1,2) this tells us that the x coordinate of the centre is 1 and the y coordinate of the centre is 2, hence a=1 and b=2. So we know have our equation looking like this: (x-1)2+(y-2)2=r2 Now to find r, the radius, we use the point we are given on the circle. Because we are told this point lies on the circle it must satisfy our equation. This means that when we substitute in the given x and y coordinates into our equation we will get what r2 is equal to. For example, if the given point on the cirlce is (5,6) we will get (5-1)2+(6-2)2=r2 Hence, r2=32. So our final answer is (x-1)2+(y-2)2=32. However it is important to notice that if you are asked for the radius it is not just simply 32, it will be the sqrt of 32 as 32=r2
