2026 TKGS WA2 Q4

The equation of a curve is \(y=ax+\dfrac bx-1\), where \(a\) and \(b\) are constants.

The normal to the curve at the point \(S(1,3)\) is parallel to the line \(x+2y=10\). This normal meets the curve again at point \(T\).

1. Show that \(a=3\) and \(b=1\).[5]
2. Find the coordinates of point \(T\).[4]