A curve has equation xy = 12 + x and a line has equation y = kx

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A curve has equation xy = 12 + x and a line has equation y = kx − 9, where k is a constant.

a. In the case where k = 2, find the coordinates of the points of intersection of the curve and the line.

b. Find the set of values of k for which the line does not intersect the curve.

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