## anonymous one year ago 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.

1. anonymous

2. welshfella

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

3. alekos

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

4. anonymous

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?

5. welshfella

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

6. anonymous

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

7. welshfella

- * - = +

8. anonymous

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

9. welshfella

so how would you proceed from here?

10. anonymous

k^2=64 $k=\pm8$

11. welshfella

yep

12. anonymous

Great! Thank you.