1.28: Integration and normal meeting a horizontal line

0606/12/M/J/16 — Question 9 · 10 marks

A curve passes through the point (2,−43)\left(2, -\dfrac{4}{3}\right) and is such that dydx=(3x+10)−12\dfrac{\mathrm{d}y}{\mathrm{d}x} = (3x + 10)^{-\frac{1}{2}}.
(i)
Find the equation of the curve.
[4]
(ii)
The normal to the curve, at the point where x=5x = 5, meets the line y=−53y = -\dfrac{5}{3} at the point PP. Find the xx-coordinate of PP.
[6]