The curve \(C\) has equation
$$y = \frac { ( x - a ) ( x - b ) } { x - c }$$
where \(a , b , c\) are constants, and it is given that \(0 < a < b < c\).
- Express \(y\) in the form
$$x + P + \frac { Q } { x - c }$$
giving the constants \(P\) and \(Q\) in terms of \(a , b\) and \(c\).
- Find the equations of the asymptotes of \(C\).
- Show that \(C\) has two stationary points.
- Given also that \(a + b > c\), sketch \(C\), showing the asymptotes and the coordinates of the points of intersection of \(C\) with the axes.