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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.

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  1. anonymous
    • one year ago
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  2. welshfella
    • one year ago
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    there is an error on the second line 2x + 8/x = k 2x^2 + 8 = kx

  3. alekos
    • one year ago
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    that's pretty close but b^2 - 4ac = k^2 - 64

  4. anonymous
    • one year ago
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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?

  5. welshfella
    • one year ago
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    no b^2 = (-k)^2 = k^2

  6. anonymous
    • one year ago
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    so because its squared it will be positive anyway and you can change the sign?

  7. welshfella
    • one year ago
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    - * - = +

  8. anonymous
    • one year ago
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    Ok, just making sure :) Thanks for all the help on this question!

  9. welshfella
    • one year ago
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    so how would you proceed from here?

  10. anonymous
    • one year ago
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    k^2=64 \[k=\pm8\]

  11. welshfella
    • one year ago
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    yep

  12. anonymous
    • one year ago
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    Great! Thank you.

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