The equation of a line is y = x k, where k is a constant, and

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The equation of a line is y = x − k, where k is a constant, and the equation of a curve is x² + 2y = k.

a) When k = 1, the line intersects the curve at the points A and B. Find the coordinates of A and the coordinates of B.

b) Find the value of k for which the line y = x − k is a tangent to the curve x² + 2y = k.

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