2.55: Normal gradient and tangent to a rational curve

0606/22/O/N/19 — Question 5 · 7 marks

At the point where x=1x = 1 on the curve y=k(x+1)2y = \dfrac{k}{(x + 1)^{2}}, the normal has a gradient of 13\dfrac{1}{3}.
(i)
Find the value of the constant kk.
[4]
(ii)
Using your value of kk, find the equation of the tangent to the curve at x=2x = 2.
[3]