2.1: Curve meets a line; perpendicular bisector

0606/21/M/J/17 — Question 9 · 9 marks

The curve 3x2+xy−y2+4y−3=03x^{2} + xy - y^{2} + 4y - 3 = 0 and the line y=2(1−x)y = 2(1 - x) intersect at the points AA and BB.
(i)
Find the coordinates of AA and of BB.
[5]
(ii)
Find the equation of the perpendicular bisector of the line ABAB, giving your answer in the form ax+by=cax + by = c, where aa, bb and cc are integers.
[4]