+129852 4x^2 + 3y^2 -16x + 9y + 16 = 0 rearrange as
4x^2 - 16x + 3y^2 + 9y = -16 complete the square on x and y
4(x^2 - 4x + 4) + 3(y^2 + 3y + 9/4) = -16 + 16 + 27/4
4 (x - 2)^2 + 3(y + 3/2)^2 = 27/4 multiply through by 4/27
(16/27)(x - 2)^2 + (12/27)(y + 3/2)^2 = 1
16(x - 2)^2 12 (y + 3/2)^2
_______ + _________ = 1
27 27
16 ( x - 2)^2 4(y + 3/2)^2
__________ + __________ = 1
27 9
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