Circle

Definition

A circle is the set of all points in a plane that are the same distance from a fixed centre.

Used by AQA, Edexcel and OCR

Specification A16 · Paper 1, Paper 2, Paper 3

A circle is the set of all points that are the same distance from a fixed point called the centre.
A circle consists of all the points that are a fixed distance from its centre.
Revise: Circle Equations

Specification A16 · Paper 1, Paper 2, Paper 3

1
Check that the stated point lies on the circle before using it: substitute its coordinates into $x^2+y^2=r^2$ .

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Specification 7.01f · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)

A set of points in a plane that are all the same distance from one fixed point.
This explains the circle's symmetry in both coordinate axes.
Revise: Circle Equations

Before finding a tangent, substitute the given point into the circle equation if you are asked to show—or need to check—that it lies on the circle.

The shortcut $ax+by=r^2$ applies to the tangent at $(a,b)$ only when the circle is centred at the origin and $a^2+b^2=r^2$ .