2026 NASS P1 Q9

The points \(A\) and \(B\) have coordinates \((5,7)\) and \((13,1)\) respectively. A point \(P\) moves such that \(PA=PB\). The set of all possible positions of \(P\) satisfying \(PA=PB\) forms a straight line, \(L\).

1. Show that the equation of \(L\) is given by \(y=\dfrac43x-8\).[3]
2. \(L\) intersects the \(x\)-axis at \(H\) and the \(y\)-axis at \(K\). A circle \(C\) passes through the three points \(O\), \(H\) and \(K\), where \(O\) is the origin. Linabell claims that the circumference of \(C\) is greater than 30 units. Determine if Linabell is correct.[4]