How do i find the center of an ellipse in this form

4x^2 + y^2 -4x + 4y - 11 = 0

i'm thinking of converting it to the general equation of x^2/a^2 + y^2/b^2=1 but get to this:
4x(x-1) + y(y+4) = 11

the answer is(1/2, -2)

thank you!

First, group your x's and y's together:

4x^2 - 4x + y^2 + 4y = 11. We did the adding of 11 to each side.

Factor a 4 from the x:

4(x^2 - x) + y^2 + 4y = 11

Complete the square. That's what you are doing wrong. You'll do this for both x and y:

4(x^2 - x + 1/4) + y^2 + 4y + 4 = 11 + 1 + 4

We end up with:

4(x - (1/2))^2 + (y + 2)^2 = 16

Diving by 16 leads to:

(x - (1/2))^2 / 4 + (y+2)^2/16 = 1

Now, you can get the center. Remember, you don't factor the variables, you must complete the square for them.

Miss Kristin