| Exam Board | CAIE |
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | June |
| Topic | Polynomial Division & Manipulation |
9 The curve \(C\) has equation
$$y = \frac { x ^ { 2 } - 2 x + \lambda } { x + 1 }$$
where \(\lambda\) is a constant. Show that the equations of the asymptotes of \(C\) are independent of \(\lambda\).
Find the value of \(\lambda\) for which the \(x\)-axis is a tangent to \(C\), and sketch \(C\) in this case.
Sketch \(C\) in the case \(\lambda = - 4\), giving the exact coordinates of the points of intersection of \(C\) with the \(x\)-axis.