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Equation of a Circle
Equation of a Circle
What is the equation of a circle?
A circle centered on the origin with radius
r
has equation
x
2
+ y
2
= r
2
(a, b)
lies on the circle if
a
2
+ b
2
= r
2
If
a
2
+ b
2
< r
2
then (a, b) lies
inside
the circle
If
a
2
+ b
2
> r
2
then (a, b) lies
outside
the circle
The circle cuts the
x
- and
y
-axes at
±r
(“plus or minus r”)
The diameter = 2r and the circumference = 2πr
Exam Tip
if asked for the radius, don't forget to square root r
2
e.g. for
x
2
+
y
2
= 10, the radius is √10, not "10"
Worked example
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