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Equation of a Circle (OCR GCSE Maths)
Revision Note
Equation of a Circle
What is the equation of a circle?
- A circle centered on the origin with radius r has equation x2 + y2 = r2
- (a, b) lies on the circle if a2 + b2 = r2
- If a2 + b2 < r2 then (a, b) lies inside the circle
- If a2 + b2 > r2 then (a, b) lies outside the circle
- The circle cuts the x- and y-axes at ±r (“plus or minus r”)
- The diameter = 2r and the circumference = 2πr
Examiner Tip
- if asked for the radius, don't forget to square root r2
- e.g. for x2 + y2 = 10, the radius is √10, not "10"
Worked example
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