Circles

The Equation of a Circle

As seen previously, the equation of the circle is (x-a)²+(y-b)²=r², where (a,b) is the centre of the circle, and r is the radius of the cirle. If you want to express a circle equation in that form, for example x²+6x+y²-2y+6=0, then you have to complete the square for both x and y. This gives you (x+3)²+(y-1)²-9-1+6=0, giving the overall equation of (x+3)²+(y-1)²=4, so the circle has radius 2 centered about (-3,1).

Circle Theorems

Thi is a recap of some of the circle theorems from GCSE Maths

• The angle formed in a semicircle when two lines meet from the edge is 90 degreees
• The perpendicular from the centre to a chord bisects the chord
• The tangent to a circle is perpendicular to the radius where they meet