Find the equation of the line passing through \(\mathrm { A } ( - 1,1 )\) and \(\mathrm { B } ( 3,9 )\).
Show that the equation of the perpendicular bisector of AB is \(2 y + x = 11\).
A circle has centre \(( 5,3 )\), so that its equation is \(( x - 5 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = k\). Given that the circle passes through A , show that \(k = 40\). Show that the circle also passes through B .
Find the \(x\)-coordinates of the points where this circle crosses the \(x\)-axis. Give your answers in surd form.