Let M(x1, y1) be the midpoint of a chord of y2 = 16x. Hence, the equation of the chord is
yy1 - 8(x + x1) = y12 - 16x1
This chord passes through the vertex (0, 0). This implies
- 8x1 = y12 - 16x1
= y12 - 8x1
Therefore, the locus of M(x1, y1) is the parabola y2 = 8x. Hence, the length of latus rectum is 8.