IAL 2026 Jan A FP1 Q3

Question

[!problem]

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.

The rectangular hyperbola $H$ has parametric equations

$x = 4t, \quad y = \frac{4}{t}$

The straight line with equation $3y - 2x = 10$ intersects $H$ at the points $A$ and $B$.

Given that the point $A$ is above the $x$-axis,

(a) find the coordinates of the point $A$ and the coordinates of the point $B$.

(5)

(b) Find the coordinates of the midpoint of $AB$.

(2)