9. (a) On separate axes sketch the graphs of
- \(y = - 3 x + c\), where \(c\) is a positive constant,
- \(y = \frac { 1 } { x } + 5\)
On each sketch show the coordinates of any point at which the graph crosses the \(y\)-axis and the equation of any horizontal asymptote.
Given that \(y = - 3 x + c\), where \(c\) is a positive constant, meets the curve \(y = \frac { 1 } { x } + 5\) at two distinct points,
(b) show that \(( 5 - c ) ^ { 2 } > 12\)
(c) Hence find the range of possible values for \(c\).