Explanation

(d)
If $P\left( at^{2},\ 2at \right)$ be one end of a focal chord of the parabola $y^{2} = 4ax$, then another end of chord will be $\mathcal{Q}\left( \frac{a}{t^{2}},\frac{- 2a}{t} \right)$
$\therefore$ Length of focal chord$= P\mathcal{Q}$
$= \sqrt{\left( \frac{a}{t^{2}} - at^{2} \right)^{2} + \left( - \frac{2a}{t} - 2at \right)^{2}}$
$= a\left( \frac{1}{t} + t \right)\sqrt{\left( \frac{1}{t} - t \right)^{2} + 4}$
$= a\left( \frac{1}{t} + t \right)^{2}$