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Thread: Line & Circle?

  1. Jun 30th, 2001, 02:52 AM #1
    Vlatko
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    Question Line & Circle?

    For which value of k the line x = k*y touches the circle
    x^2 + y^2 - 10y + 16 = 0 in one point.
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  2. Jun 30th, 2001, 04:04 AM #2
    Sam Finch
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    The way to do this is to find a polynomial in y for which the line crosses the circle at it's roots, eg



    we now need to find the values of k for which there is only one solution, eg 100-64(k²+1) = 0

    solve that and you have your answer.
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  3. Jun 30th, 2001, 06:31 AM #3
    Vlatko
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    Yes, k is +3/4 or -3/4. I thought so . Thanks.
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