Given : The equation of parabola is y² = 16x

Equation chord is

2x + y = p ..... (1)

Equation of chord with middle point (h, k) is given as

$$ky - 16\left( {{{x + h} \over 2}} \right) = {k^2} - 16h$$

$$ \Rightarrow ky - 8(x + h) = {k^2} - 16h$$

$$ \Rightarrow ky - 8x - 8h = {k^2} - 16h$$

$$ \Rightarrow ky - 8x - 8h - {k^2} + 16h = 0$$

$$ \Rightarrow - 8x + ky + 8h - {k^2} = 0$$

$$ \Rightarrow 8x - ky = 8h - {k^2}$$ ..... (2)

Comparing above equation with equation of chord, we get

$$2x + y = p$$

Dividing Eq. (2) by 4, we get

$${{8x} \over 4} - {{ky} \over 4} = {{8h} \over 4} - {{{k^2}} \over 4}$$

$$2x - {{ky} \over 4} = 2h - {{{k^2}} \over 4}$$

On comparing, we get

$$ \Rightarrow {{ - k} \over 4} = 1$$ and $$p = 2h - {{{k^2}} \over 4}$$

$$ \Rightarrow k = - 4$$ and $$p = 2h - {{{{( - 4)}^2}} \over 4} = 2h - 4$$

$$ \Rightarrow p = 2h - 4 \Rightarrow 2h - p = 4$$

Only p = 2 and h = 3 satisfies this equation. Therefore, p = 2, h = 3 and k = $$-$$4.