The equation of a curve is xy=8 and the equation of a line is 2x+y=k, where k is a constant. Find the values of k for which the line forms a tangent to the curve.
I don't really know how to approach this question, I think I am just missing a few steps. Will post what I tried too.

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there is an error on the second line
2x + 8/x = k
2x^2 + 8 = kx

that's pretty close but b^2 - 4ac = k^2 - 64

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