So I assume b is (-1, 0).

I am not sure what the "length of chord on x-axis" is: the projection of the chord to the x-axis? Why are you interested in it since it is not known that the chord is parallel to the x-axis? Also, "Let |ab| = " is ambiguous. Does this mean that or , or maybe does not lie on the x-axis at all?

Hint: The line from the circle center to the chord center is perpendicular to the chord. Using this fact, find a right triangle with a radius as the hypotenuse.