A ray of light travels parallel to the axis of the parabolic mirror y² = 16x along the line y = 4…

Step 1. The point $P$. $2at = 8t = 4$, so $t = \dfrac{1}{2}$. Then $P = (4 \times \tfrac{1}{4}, 4) = (1, 4)$.

Step 2. The reflection. After reflection the ray goes through the focus $(4, 0)$. So $PQ$ is a focal chord and $Q$ has the parameter $t' = -\dfrac{1}{t} = -2$. Then $Q = (4 \times 4, 8 \times (-2)) = (16, -16)$.

Step 3. The length. $PQ = a\left(t + \dfrac{1}{t}\right)^2 = 4 \times \left(\dfrac{1}{2} + 2\right)^2 = 25$ centimetres. As a check, $FP = 5$ and $FQ = 20$, and they add to $25$.