4
\includegraphics[max width=\textwidth, alt={}, center]{074597e7-5bb1-4249-9cfa-784974a6fd2b-2_947_1305_986_420}
The diagram shows the curve with equation
$$y = \frac { a x + b } { x + c }$$
where \(a , b\) and \(c\) are constants.
- Given that the asymptotes of the curve are \(x = - 1\) and \(y = - 2\) and that the curve passes through \(( 3,0 )\), find the values of \(a , b\) and \(c\).
- Sketch the curve with equation
$$y ^ { 2 } = \frac { a x + b } { x + c }$$
for the values of \(a , b\) and \(c\) found in part (i). State the coordinates of any points where the curve crosses the axes, and give the equations of any asymptotes.