2.34: Normal to a quadratic curve

0606/22/M/J/17 — Question 4 · 6 marks

The point PP lies on the curve y=3x27x+11y = 3x^{2} - 7x + 11. The normal to the curve at PP has equation 5y+x=k5y + x = k. Find the coordinates of PP and the value of kk.
[6]