2.48: Curve from normal gradient and tangent equation

0606/22/O/N/17 — Question 7 · 9 marks

The gradient of the normal to a curve at the point with coordinates (x,y)(x, y) is given by x1−3x\dfrac{\sqrt{x}}{1 - 3x}.
(i)
Find the equation of the curve, given that the curve passes through the point (1,−10)(1, -10).
[5]
(ii)
Find, in the form y=mx+cy = mx + c, the equation of the tangent to the curve at the point where x=4x = 4.
[4]