Answer only one of the following two alternatives. OR A curve C has parametric equations x = 1 − 3t², y = t(1 – 3t²), for 0 ≤ t ≤ 1/√3. Show that (dx/dt)² + (dy/dt)² = (1+9t²)². Hence find (i) the arc length of C, (ii) the surface area generated when C is rotated through 2π radians about the x-axis. Use the fact that t = y/x to find a cartesian equation of C. Hence show that the polar equation of C is r = sec θ(1 – 3 tan²θ), and state the domain of θ. Find the area of the region enclosed between C and the initial line.