2024 NYJC Promo Q3

The curve \(D\) has equation \(y = \frac{2x - 5}{x^2 + 2x - 3}.\)

1. Sketch the graph of \(D\), stating the equations of any asymptotes, the coordinates of the points where the curve crosses the axes and the stationary point(s).[3]
2. By considering a suitable curve, hence, find the exact range of values of \(k\), where \(k > 0\), such that the equation \((x + 3)^2 + \left( \frac{2x - 5}{x^2 + 2x - 3} \right)^2 = k^2\) has at least one positive real root.[3]