Multiple choice

The locus of middle points of the chords of the circle $x^2 + y^2$ + 2gx + 2fy + c = 0, which pass through a fixed point (a,b) is :

$x^2 + y^2$ + x(a-g) + (b-f) - ag - bf =0
$x^2 + y^2$ + x(a-g) + y(b +f) - ag - bf = 0
$x^2 + y^2$ - x(a-g) - y(b-f) - ag - bf = 0
$x^2 + y^2$ - x(a-g) - y(b-f) + ag + bf = 0

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