If b and c are the lengths of the segments of any focal chord of a parabola $y^2=4ax$, then the length of the semi-latus rectum is :

Question

$$\begin {array} {1 1} (a)\;\frac{bc}{b+c} & \quad (b)\;\sqrt {bc} \\ (c)\;\frac{b+c}{2} & \quad (d)\;\frac{2bc}{b+c} \end {array}$$