I am trying to find the standard form of this equation for an ellipse.
9x^2 + 4y^2 - 36x + 8y + 31 = 0
First I grouped the x and y's together.
9x^2 - 36x + ? + 4y^2 + 8y + ? = -31 + ? + ?
Then I factored the 9 and 4.
9(x^2-4x+4) + 4(x^2+2x+1) = -31+36+4
9(x-2)^2 + 4(x-1)^2 = 9
Then I divided it all by 9 and got:
(x-2)^2 / 1 + 4(x-1)^2 / 9 = 1
Is this correct or did I mess up somewhere?