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Can someone please solve these 2 equations to get values of h and k? I know the values of h and k but not sure how to solved these equations to get h and k 's values

  1. $(20.01 - h)^2 + (17.94 - k)^2 = 285.27$
  2. $(3.25 - h)^2 + (15.81 - k)^2 = 285.27$

These equations are of a circle representing 2 points on circumferences. Answer is $h = 13.45$ $k = 2.36$

  • 4
    Are you asking for a solution for $h$ and $k$ in terms of $r$? Please clarify.2012-01-06
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    The two equations are not enough to solve for $h$ and $k$ without knowing what $r$ is. There are infinitely many distinct circles that go through the points $(20.01,17.94)$ and $(3.25,15.81)$, and so the two equations, by themselves, cannot uniquely determine $h$ and $k$.2012-01-06
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    Ok here is the value of r^2 = 285.272012-01-06
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    Are you sure there's only one solution for $(h, k)$?2012-01-06
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    @coure2011: There are two solutions for each value of $r$.2012-01-06
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    There are 0, 1, or 2 solutions, depending on r, since this problem is exactly the same as finding the intersection of two circles with different centers.2012-01-06

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