Here's the FULL SOLUTION, only doing this because this is the one of the two questions i've been able to do in the marathon =(, also I dunno, if Anchovies still wants to know how to do it, (assuming he doesn't...)
(a) Implicit diffrentiation:
2x/a^2 - 2yy'/b^2 = 0
y' = (2x/a^2)*(b^2/2y)
y' =...