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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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.

Mathematics
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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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Ok, if I fix that mistake though I get 2x^2-kx+8=0 right? So wouldn't that mean that b^2-4ac= -k^2 -64?
no b^2 = (-k)^2 = k^2
so because its squared it will be positive anyway and you can change the sign?
- * - = +
Ok, just making sure :) Thanks for all the help on this question!
so how would you proceed from here?
k^2=64 \[k=\pm8\]
yep
Great! Thank you.

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