Question

3x^2 + 3y^2-6x+12y=0 as a perfect square

Answer 1

first divide through by 3

Answer 2

Post your result and we can go from there.

Answer 3

Do I divide all by three

Answer 4

yes

Answer 5

Okay I got x^2 +y^2 - 2x+4y=0

Answer 6

Now we are going to complete the square twice. So focus first on x^2-2x
Complete the square on that.

Answer 7

So its (x+1)^2

Answer 8

(x-1)^2

Answer 9

Oh okay

Answer 10

And since you added 1 to the left side, you need to add 1 to the right side as well.

Answer 11

Now complete the square on the y^2+4y

Answer 12

Wait u get 1 by dividing 2 and then squaring it right

Answer 13

divide 4 by 2 and that is 2. Square the result and you have 4. So add 4 to both sides

Answer 14

So 0 is now 5

Answer 15

And now you have:
\[(x-1)^2+(y+2)^2=5\]

Answer 16

And that is a circle with center (1,-2) and radius sqrt5

Answer 17

And that's the answer