Poncelet's porism on non-circular conic sections

Introduction Poncelet&rsquo;s porism or Poncelet&rsquo;s closure theorem is one of the most remarkable results in plane geometry. It is most easily described in terms of circles: suppose we have two circles \(C\) and \(D\), with \(D\) lying entirely inside \(C\). Pick a point \(p_0\) on \(C\), and find the tangent from \(p_0\) to \(D\). Let \(p_1\) be the other intersection of the tangent line at…