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Year 9 · Functions & Graphs

Circles in the coordinate plane

A circle with centre (a, b) and radius r has equation (x − a)² + (y − b)² = r².

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How to do it

  1. Centre: the numbers inside the brackets, with signs flipped.
  2. Radius: square root of the right-hand side.

Worked example

What is the centre of the circle (x + 5)² + (y − 4)² = 25?
In (x − a)² + (y − b)² = r² the centre is (a, b). Watch the signs: (-5, 4).
Answer: (-5, 4)

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(y + 2) means b = −2.

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