A curve has equation xy = 20 and a line has equation x + 2y = k,

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A curve has equation xy = 20 and a line has equation x + 2y = k, where k is a constant.

a. In the case where k = 14, the line intersects the curve at the points A and B.

Find:

i. The coordinates of the points A and B.

ii. The equation of the perpendicular bisector of the line AB.

b. Find the values of k for which the line is a tangent to the curve.

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