The equations of the sides \( AB \) and \( AC \) of a triangle \( ABC \) are \( (\lambda + 1)x + \lambda y = 4 \) and \( \lambda x + (1-\lambda)y + \lambda = 0 \) respectively. Its vertex \( A \) is on the y-axis and its orthocentre is \( (1, 2) \). The length of the tangent from the point \( C \) to the part of the parabola \( y^{2} = 6x \) in the first quadrant is:
