2026 MSHS P1 Q13

A telecommunications company is setting up a circular coverage zone. Two engineers are at points \(A(5,3)\) and \(B(-1,3)\) on the perimeter of the circle. The centre of the coverage zone lies on the line \(y=2x-5\).

1. Find the equation of the circle in the form \(x^2+y^2+2gx+2fy+c=0\).[6]
2. A signal booster is placed at the point \((2,m)\) inside the coverage zone. Find the range of values of \(m\).[2]