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.(adsbygoogle = window.adsbygoogle || []).push({});

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...

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# Intersection of ellipses and equivalent problems

Can you offer guidance or do you also need help?

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