Coordinate Geometry
The Equation Of A Circle

Knowledge needed of Completing The Square

Equation Of A Circle
(x - a)2 + (y - b)2 = r2
where
a is the x co-ordinate of the centre of the circle
b is the y co-ordinate of the centre of the circle
r is the radius of the circle

In terms of showing method and avoiding error
especially with directed numbers
the following format can be very useful
[x - (a)]2 + [y - (b)]2 = (r)2

Example
 
(x + 2)2 + (y - 3)2 = 52
 
[x + 2]2 + [y - 3]2 = 52
 
[x - (-2)]2 + [y - (3)]2 = (5)2
 
a = (-2)
-2 is the x co-ordinate
of the centre of the circle
b = (3)
3 is the y co-ordinate
of the centre of the circle
r = (5)
5 is the radius
of the circle

Equation of a circle where the center of the circle is at the origin (0,0)

Equation of a circle where the center of the circle is not at the origin

Writing the equation of a circle when given the center and radius

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