What is major axis for the equation 9x^2 + 16y^2 - 36x + 96y + 36 = 0

Answer 1

I will complete the square for you for this ellipse, you should be able to figure it from there

9(x^2 -4x + ...) + 16(y^2 + 6y + ...) = -36
9(x^2 - 4x + 4) + 16(y^2 + 6y + 9) = -36 + 36 + 144
9(x-2)^2 + 16(y+3)^2 = 144
(x-2)^2/16 + (y+3)^2/9 = 1