This is the equation of an ellipse.
I assume you want it in standard form
complete the square
x^2 + 4x + 4 + 9(y^2 - 4y + 4) = -4 + 4 + 36
(x+2)^2 + 9(y-2)^2 = 36
divide both sides by 36
(x+2)^2 /36 + (y-2)^2 /4 = 1
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