The parametric equation of an ellipse is given by x a cost

Question

1. The curve x = t² - t, y = t³ - 3t - 1 crosses itself at (2,1). Determine equations of the tangent lines at that point.

2. The parametric equation of an ellipse is given by x = a cos(t), y = b sin(t); 0 ≤ t ≤ 2π. Determine the area inside the ellipse in terms of a and b.

3. Find the length of the asteroid given by the parametric equations; x = cos³(t), y = sin³(t), 0 <= t <= 2π.