What is the radius of a circle whose equation is x^2+y^2-10x+6y + 18=0

We must write this equation in the form

(

x

-

a

)

2

+

(

y

-

b

)

2

=

r

2

Where

(

a

,

b

)

are the co ordinates of the center of the circle and the radius is

r

.

So the equation is

x

2

+

y

2

-

10

x

+

6

y

+

18

=

0

Complete the squares so add 25 on both sides of the equation

x

2

+

y

2

-

10

x

+

25

+

6

y

+

18

=

0

+

25

=

(

x

-

5

)

2

+

y

2

+

6

y

+

18

=

0

+

25

Now add 9 on both sides

(

x

-

5

)

2

+

y

2

+

6

y

+

18

+

9

=

0

+

25

+

9

=

(

x

-

5

)

2

+

(

y

+

3

)

2

+

18

=

0

+

25

+

9

This becomes

(

x

-

5

)

2

+

(

y

+

3

)

2

=

16

So we can see that the centre is

(

5

,

-

3

)

and the radius is

√

16

or 4