2.4: Tangent from a line to a circle

0606/21/O/N/16 — Question 9 · 10 marks

The line y=kx4y = kx - 4, where kk is a positive constant, passes through the point P(0,4)P(0, -4) and is a tangent to the curve x2+y22y=8x^{2} + y^{2} - 2y = 8 at the point TT. Find
(i)
the value of kk,
[5]
(ii)
the coordinates of TT,
[3]
(iii)
the length of TPTP.
[2]