2.10: Tangents to a quadratic curve

0606/22/O/N/18 — Question 10 · 5 marks

Two lines are tangents to the curve y=124xx2y = 12 - 4x - x^{2}. The equation of each tangent is of the form y=2k+1kxy = 2k + 1 - kx, where kk is a constant.
(i)
Find the two possible values of kk.
[5]