Circle equation question

1. The problem statement, all variables and given/known data
A circle has equation x² + y² - 8x - 4y = 9

(i) Show that the centre of this circle is (4,2) and find the radius of the circle.


2. Relevant equations
Circle equation = (x-a)² + (x-b)² = r²


3. The attempt at a solution
Well, if the centre of the circle is (4,2). Then the equation will be something like:

(x-4)² + (y-2)² = 9

except, if I expand out the two brackets, I get

(x² -8x + 16) + (y² -4y + 4) = 9

x² - 8x + y² -4y + 20 = 9

Here is where i get confused

So (i'm just double checking here since I don't have the answers), is the radius of the circle sqr9 or sqr 11? And is this really showing that (4,2) is the centre?

Thanks

 

oops, fix'd (i hope :) )

 

Thanks for the replies, I managed to reach sqr29 using a different method though.

x² + y² - 8x - 4y = 9

so

x² + y² - 8x - 4y - 9 = 0

and the equation of a circle is

(x - a)² + (x - b)² = r²

expand out

x² + y² - 2ax - 2by + a² + b² - r²

equating coeficients

-2a = -8
a = 4

-2b = -4
b = 2

constant terms

a² + b² - r² = -9

4² + 2² - r² = -9

-r² = -29

r = sqr29

and I think that shows that the centre is (4,2) as well

This way seems logical but much longer