Official solution
For this parabola y2 = 16x,
a = 4
Here PQ is focal cord.
Let P(at12, 2at1) and Q(at22, 2at2).
Given P(1, 4),
\[ \therefore \] at12 = 1
\[ \Rightarrow \] 4t12 = 1
\[ \Rightarrow \] t12 = \[{1 \over 4}\]
\[ \Rightarrow \] t1 = \[{1 \over 2}\]
In parabola if the parameter of one end point of the focal cord is t1 then parameter of the other end point t2 = \[ - {1 \over {{t_1}}}\]
Here parameter for point Q t2 = - 2
\[ \therefore \] Length of focal cord
|PQ| = a\[{\left( {{t_1} - {t_2}} \right)^2}\] = 4\[{\left( {{1 \over 2} + 2} \right)^2}\] = 25