# determine general form equation of ellipse using (x-2)^2 /6 + (y+3)^2/4 =1

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Multiply both sides by 24 (6*4) to get

4(x-2)^2+6(y+3)^2 = 24

Expand the binomials to get

4(x^2-4x+4)+6(y^2+6y+9) = 24

Distribute

4x^2 - 16x + 16 + 6y^2 + 36y + 54 = 24

Subtract 24 from both sides and rearrange into general form

4x^2 + 6y^2 -16x + 36y + 46 = 0