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Intersection of ellipses and equivalent problems

  1. Jul 10, 2010 #1
    Does anyone know how to determine whether two ellipses intersect? I don't need the precise points but rather only the answer whether there are points. All my attempts led to 4th order polynomials, which are heavy to solve, but considering that I don't need the actual points I assume there must be an easier way.

    Some guy claims it's doable
    http://www.cut-the-knot.org/htdocs/dcforum/DCForumID6/710.shtml

    Here are some equivalent problems which have to be solved for the angles (which however I can't solve either...)
    [tex]\cos\phi+a\sin\theta=x[/tex]
    [tex]\sin\phi+b\cos\theta=y[/tex]
    or even
    [tex]\Re(e^{i\theta}(1+ze^{i\theta}))=q[/tex]
    where z is complex, is an equivalent problem. Any ideas?

    My best attempt so far was using discriminants, but it's messy and I made a mistake somewhere...
     
  2. jcsd
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