(a) Show that the points on all four of the given parametric curves satisfy the same Cartesian equation.

(i) x = t², y = t

(ii) x = t, y = √t

(iii) x = cos²t, y = cos t

(iv) x = 3^2t, y = 3^t

(b) Sketch the graph of each curve in part (a) and explain how the curves differ from one another.