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.

Question

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.

anonymous · Answer

attachment

welshfella · Answer

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

alekos · Answer

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

anonymous · Answer

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?

welshfella · Answer

no b^2 = (-k)^2 = k^2

anonymous · Answer

so because its squared it will be positive anyway and you can change the sign?

welshfella · Answer

- * - = +

anonymous · Answer

Ok, just making sure :) Thanks for all the help on this question!

welshfella · Answer

so how would you proceed from here?

anonymous · Answer

k^2=64
$$k=\pm8$$

welshfella · Answer

yep

anonymous · Answer

Great! Thank you.