7 A curve \(C\) has equation \(y = \frac { 1 } { ( x - 2 ) ^ { 2 } }\).
- Write down the equations of the asymptotes of the curve \(C\).
- Sketch the curve \(C\).
- The line \(y = x - 3\) intersects the curve \(C\) at a point which has \(x\)-coordinate \(\alpha\).
- Show that \(\alpha\) lies within the interval \(3 < x < 4\).
- Starting from the interval \(3 < x < 4\), use interval bisection twice to obtain an interval of width 0.25 within which \(\alpha\) must lie.