2.5: Tangent line to two quadratic curves

0606/21/O/N/18 — Question 10 · 8 marks

The line y=12−2xy = 12 - 2x is a tangent to two curves. Each curve has an equation of the form y=k+6+kx−x2y = k + 6 + kx - x^{2}, where kk is a constant.
(i)
Find the two values of kk.
[5]
(ii)
The line y=12−2xy = 12 - 2x is a tangent to one curve at the point AA and the other curve at the point BB. Find the coordinates of AA and of BB.
[3]