1. (8pts) Consider the parametric curve given by, C(t) = (t2 - 2t, (3 - 12t) a. Find the values of t where C passes through the point (8, 16) b. Since C passes through the point (8, 16) for two different values of t, C has two slopes at that point. Find the slopes of C at the point (8, 16). c. Find an integral representing the area of the loop of C by using either of the formulas t2 t2 t2 A = -y dx = x dy = x dy - y dx 2 t 1 t 1 t1 d. BONUS: Show that there are no other points where C intersects itself