The points of intersection of the line \( ax + by = 0, \; (a \neq b) \) and the circle \( x^2 + y^2 - 2x = 0 \) are \( A(\alpha, 0) \) and \( B(1, \beta) \). The image of the circle with \( AB \) as a diameter in the line \( x + y + 2 = 0 \) is:
\( x^2 + y^2 + 3x + 5y + 8 = 0 \)
\( x^2 + y^2 - 5x - 5y + 12 = 0 \)
\( x^2 + y^2 + 3x + 3y + 4 = 0 \)
\( x^2 + y^2 + 5x + 5y + 12 = 0 \)
