The parametric coordinates for the line AB would be $(a+ r\cos\alpha, r\sin\alpha)$.
Let's put this coordinates in the equation $y^2=4ax$.
We get, $r^2\sin^2\alpha - 4a\cos\alpha r -4a^2=0$
Sum of roots=AB= $\frac{-b}{a}=\frac{4a\cos\alpha}{(\sin\alpha)^2}$
But the right answer is AB=$\frac{4a}{(\sin\alpha)^2}$. What am I doing wrong?