2025 YIJC Promo Q9

A curve \(C\) has parametric equations

1. Sketch \(C\), indicating the coordinates of the points where the curve cuts the axes.[3]
   It is now given that \(a=1\).
2. Find the equation of the normal to the curve at the point where \(t=1\).[3]
3. Find the acute angle between the normal in part (b) and the \(x\)-axis.[2]
4. Find the equation of the tangent to the curve that is parallel to the \(y\)-axis.[2]