1.44: Normal to a logarithmic curve and triangle area

0606/12/O/N/16 — Question 5 · 7 marks

(i)
Find the equation of the normal to the curve y=12ln(3x+2)y = \dfrac{1}{2}\ln(3x + 2) at the point PP where x=13x = -\dfrac{1}{3}.
[4]
(ii)
The normal to the curve at the point PP intersects the yy-axis at the point QQ. The curve y=12ln(3x+2)y = \dfrac{1}{2}\ln(3x + 2) intersects the yy-axis at the point RR. Find the area of the triangle PQRPQR.
[3]