A curve passing through the point P (0,1) has an equation y = f (x) which satises the condition dzy dy 2 am- 1+ (3) where a is a constant. (a) Show that the function y = g (8%: + 3-2) satises the above condition, and nd the value of a. (3 marks) (b) A variable point M (x, y) initially at P moves on the curve in (a), where x 2 0 . The normal at M to the curve cuts the yaxis at N. The circle with centre N and the radius NM touches the curve and has an area A square units. (i) Let R be the radius of the circle. Find R in terms of x. (ii) It is given that M moves so that its y-coordinate increases at a rate of 2 units per second. xex(e2x+1)(e4x4xe2x1)) (92x_1)4 dA _ (1) Show that E 81r( (2) Find the rate of change of A after 0.125 seconds, correct your answer to 4 sig. g. (10 marks)