Radius and coord of center of a circle

[lucifer_x]

Homework Statement

9x² + 9y² - 6x + 12y - 22 = 0

Homework Equations

The Attempt at a Solution

i got this far but can't finish i don't know what to do:

3(3x² - 2x + 1) + 3(3y² + 4y + 4) = 40

 

[e(ho0n3]

Why not divide first by 9 to remove the pesky 9 in front of the square terms. Then try completing the squares.

 

[lucifer_x]

ok let me try, thanks

then its all fractions:

x² - 2/3x + y² + 4/3 = 22/9

 

[e(ho0n3]

Right. Now complete the square of x² - 2/3x and y² + 4/3.

 

[lucifer_x]

i don't know what half of 2/3 is or 4/3 because if i know that then i can square them and that's it

i calculated :

(x² - 2/3x + 1/9) + (y² + 4/3 + 2/3) = 22/9

is this it

 

[e(ho0n3]

That should be 4/3y by the way and the 2/3 term should be squared. You're almost done. Now write (x² - 2/3x + 1/9) as (x - ?)² and do the same with the other term.

 

[Mentallic]

i don't know what half of 2/3 is or 4/3 because if i know that then i can square them and that's it

It's quite simple really. half of 2/3 => $$\frac{2}{3}\div \frac{2}{1}=\frac{2}{3}x\frac{1}{2}$$
now multiply both numerator and denominators together => $$\frac{2}{6}=\frac{1}{3}$$

Similarly for 4/3. So half of 2/3 is 1/3 and half of 4/3 is 2/3. Sounds logical right?