Parabola Part 1

The equations of the sides AB and AC of a triangle ABC are (λ+1)x+λy=4 and λx+(1−λ)y+λ=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 y2=6x in the first quadrant is