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22 Dec 2025

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Understanding the Circle Equation for A-Level Maths

anna🦋🧬📓🔬

@biannnl

Coordinate geometry brings circles into the world of algebra, giving... Show more

CIRCLES-COORDINATE GEOMETRY
THE EQUATION OF
Centre: (a, b)
Badius: r
__€.g Centre: (3,-4)
Radius: 5
CIRCLE
(x-a)² + (y-b)² = r²7
-(x - 3)² +

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!

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22 Dec 2025

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1 page

Understanding the Circle Equation for A-Level Maths

anna🦋🧬📓🔬

@biannnl

Coordinate geometry brings circles into the world of algebra, giving you powerful tools to work with circular shapes using equations. Once you master the standard form of a circle's equation, you'll be able to find centres, radii, and solve complex... Show more

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The Equation of a Circle

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