Perpendicular bisector of intersection points

A question is this type if and only if it asks to find the perpendicular bisector of the line segment joining two intersection points.

1 questions · Moderate -0.3

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CAIE P1 2012 June Q10
9 marks Moderate -0.3
The equation of a line is \(2y + x = k\), where \(k\) is a constant, and the equation of a curve is \(xy = 6\).
  1. In the case where \(k = 8\), the line intersects the curve at the points \(A\) and \(B\). Find the equation of the perpendicular bisector of the line \(AB\). [6]
  2. Find the set of values of \(k\) for which the line \(2y + x = k\) intersects the curve \(xy = 6\) at two distinct points. [3]