2024 CGSS P2 Q8

A circle has a diameter \(AB\). The point \(A\) has coordinates \((1, -6)\) and the equation of the tangent to the circle at \(B\) is \(3x + 4y = k\).

1. Show that the equation of the normal to the circle at the point \(A\) is \(4x - 3y = 22\).[3]

It is also given also that the line \(x = -1\) touches the circle at the point \((-1, -2)\).

2. Find the coordinates of the centre and the radius of the circle.[4]
3. Find the value of \(k\).[3]