Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 15: Circles 211

But let’s go back to the distance formula for just
another minute. dxx yy 21 ^2  212. You
know one point is the origin, (0,0), and the dis-
tance is 5. Let’s plug those in.

Now drop the little twos at the bottom of the x
and y, and then square both sides to get rid of the
square root.

Do you know what that is? It’s the equation of the
following circle—a circle with a center at (0,0)
and a radius of 5.

50 0

5

2

2

2

2

2

2

2

2

xy

xy

 

5

5

25

22

222

22

xy

xy

xy











-6 -2 062

-2

2

4

6

-4

-6

-7 -5 -4 -1-3 -1 134 5 7

-3

-5

-7

1

3

5

7

y

x

The equation of a circle with center (0,0)

and radius r is x^2 + y^2 = r^2.

If the center isn’t at the origin, the equation

gets a little more complicated, but in a way

that makes sense if you remember that it

came from the distance formula. Suppose

you wanted a circle of radius 5 with its

center at (1,4). The equation would be (x –

1)^2 + (y – 4)^2 = 5^2. The equation of a circle

with center at (h,k) and radius r is (x – h)^2 +

(y – k)^2 = r^2.