Circles
Key Facts
You must learn the following:[br][br][list][*]The equation of a circle with centre [math](a,b)[/math] and radius [math]r[/math] is given by[math](x-a)^2+(y-b)^2=r^2[/math][/*][*]If the equation is given in expanded form, eg. [math]x^2+y^2+6x+8y-11=0[/math], then it is necessary to [b]complete the square[/b] before identifying the centre and radius:[/*][/list]
Test Yourself - Equation of a Circle
Relevant Circle Theorems
A [b]tangent[/b] to the circle will meet the [b]radius[/b] at a right-angle.[br][size=85](Gradient of radius is usually calculated easily from a known point on the circle, P, and the centre of the circle, C).[/size]
The length from a point along a tangent can form a right-angled triangle.
A chord will be [b]perpendicularly bisected [/b]by a specific radius.