在曲面上经过一点有无数条圆锥曲线

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经过曲面$x^2 y^2 + y^2 z^2 + z^2 x^2 - xyz = 0$上的每一个点，都有无数条在曲面上的圆锥曲线。如何证明？

来源：

Oxford Mathematical Institute / Models of Geometric Surfaces / Quartic Surfaces / Steiner's Surface
At each point on Steiner's surface, there are infinitely many conics lying on the surface which pass through that point