IAL 2026 Jan FP1 Q4

Question

[!problem]

The parabola $C$ has equation $y^2 = 8x$.

The line $l$ passes through the focus of $C$, has gradient $\dfrac{8}{15}$, meets $C$ at the point $G$ where $y > 0$ and meets $C$ at the point $H$ where $y < 0$.

(a) Determine the coordinates of $G$ and the coordinates of $H$.

(6)

The midpoint of the line segment $GH$ is $M$.

(b) Determine the shortest distance from $M$ to the directrix of $C$.

(2)