Answer :
18x^2 + 2x + y^2 = 1
==> 18(x^2 + x/9) + y^2 = 1
==> 18(x^2 + x/9 + 1/324) + y^2 = 1 + 1/18
==> 18(x + 1/18)^2 + y^2 = 19/18
==> (x + 1/18)^2/19 + (y - 0)^2/(19/18) = 1.
By comparing this to the standard form of an ellipse, the center is at (-1/18, 0).
==> 18(x^2 + x/9) + y^2 = 1
==> 18(x^2 + x/9 + 1/324) + y^2 = 1 + 1/18
==> 18(x + 1/18)^2 + y^2 = 19/18
==> (x + 1/18)^2/19 + (y - 0)^2/(19/18) = 1.
By comparing this to the standard form of an ellipse, the center is at (-1/18, 0).