algebra
posted by bill .
x^2 +4x +9y^2 36y +4=0

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(y2)^2 = 36
divide both sides by 36
(x+2)^2 /36 + (y2)^2 /4 = 1