- A curve \(C\) has parametric equations
$$x = 3 + 2 \sin t , \quad y = 4 + 2 \cos 2 t , \quad 0 \leqslant t < 2 \pi$$
- Show that all points on \(C\) satisfy \(y = 6 - ( x - 3 ) ^ { 2 }\)
- Sketch the curve \(C\).
- Explain briefly why \(C\) does not include all points of \(y = 6 - ( x - 3 ) ^ { 2 } , \quad x \in \mathbb { R }\)
The line with equation \(x + y = k\), where \(k\) is a constant, intersects \(C\) at two distinct points.
- State the range of values of \(k\), writing your answer in set notation.