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If one end of a focal chord of the parabola, $y^2 = 16x$ is at $(1, 4)$, then the length of this focal chord is:
(1) $25$
(2) $22$
(3) $24$
(4) $20$
$y^2 = 16x$, $a = 4$. At $(1,4)$: $t = \frac{1}{2}$. Length of focal chord $= a\left(t + \frac{1}{t}\right)^2 = 4\left(\frac{1}{2} + 2\right)^2 = 4 \times \frac{25}{4} = 25$.
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