Understanding the Circle Equation for A-Level Maths

The Equation of a Circle

Ever wondered how mathematicians describe circles using just numbers and letters? The standard form of a circle's equation is your key: $x-a$² + $y-b$² = r². Here, (a,b) represents the centre coordinates, and r is the radius.

Let's say you've got a circle with centre $3, -4$ and radius 5. Simply plug these values into the formula: $x-3$² + $y+4$² = 25. Notice how we get +4 because we're subtracting a negative number!

But what if you're given a messy equation like x² + y² + 2x - 6y = 6? Don't panic - you just need to rearrange it. First, group your x and y terms together. Then complete the square for both variables. This transforms your equation into the standard form, revealing the centre $-1, 3$ and radius 4.

Quick Tip: When completing the square, remember to add the same value to both sides of the equation to keep it balanced!