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