2023 BTYSS 3AM EOY Q3

The equation of a curve is \({y = -x^2 + 2kx - k}\), where \({k}\) is a constant.

1. In the case where \({k = 3}\), find the set of values of \({x}\) for which the curve lies completely below the line \({y = 2}\).[3]
2. In the case where \({k < 0}\), explain if the line \({y = 2x + 1}\) is a tangent to the curve.[3]