- The curve \(C\) has equation
$$y = \frac { k ^ { 2 } } { x } + 1 \quad x \in \mathbb { R } , x \neq 0$$
where \(k\) is a constant.
- Sketch \(C\) stating the equation of the horizontal asymptote.
The line \(l\) has equation \(y = - 2 x + 5\)
- Show that the \(x\) coordinate of any point of intersection of \(l\) with \(C\) is given by a solution of the equation
$$2 x ^ { 2 } - 4 x + k ^ { 2 } = 0$$
- Hence find the exact values of \(k\) for which \(l\) is a tangent to \(C\).