Show that the \(x\)-coordinate of \(A\) satisfies the equation \(\left( m ^ { 2 } + 1 \right) x ^ { 2 } - 10 ( m + 1 ) x + 40 = 0\).
Hence determine the equation of the tangent to the circle at \(A\) which passes through \(P\). [4]
A second tangent is drawn from \(P\) to meet the circle at a second point \(B\). The equation of this tangent is of the form \(y = n x + 2\), where \(n\) is a constant less than 1 .