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Math Help - inequality question

  1. #1
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    Exclamation inequality question

    Find the values of k for which the line y=( 1/2) x + k is a tangent to the curve x^2+y^2=8k

    I tried equating the two equations together, making a new combined equation.
    from that equation, I took out it's b^2 -4ac and equated it to 0. Haha I hope you can understand what I just wrote.

    Anyway If not how should I do this question? Thank you very much!!
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  2. #2
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    Re: inequality question

    Quote Originally Posted by pumbaa213 View Post
    Find the values of k for which the line y=( 1/2) x + k is a tangent to the curve x^2+y^2=8k

    I tried equating the two equations together, making a new combined equation.
    from that equation, I took out it's b^2 -4ac and equated it to 0. Haha I hope you can understand what I just wrote.

    Anyway If not how should I do this question? Thank you very much!!
    Hello,

    all your considerations are OK.

    1. If you solve for x

    x^2+\left(\frac12 x+k\right)^2=8k

    you should come out with

    x = \frac25 \cdot \sqrt{-k} \cdot \left( \sqrt{-k} \pm 2 \sqrt{k-10} \right)

    2. This yields only one value for x if
    • k = 0: The circle degenerates into a point
    • \sqrt{-k} \pm 2 \sqrt{k-10} = 0: Solve for k!
    Thanks from pumbaa213
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  3. #3
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    Re: inequality question

    Yay got it! thank you sooo much!!
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