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Putnam 1940 B4

Source: Putnam 1940

February 22, 2022
Putnamgeometry3D geometrysphere

Problem Statement

Prove that the locus of the point of intersection of three mutually perpendicular planes tangent to the surface ax2+by2+cz2=1      (where    abc≠0)ax^2 + by^2 +cz^2 =1\;\;\; (\text{where}\;\;abc \ne 0) is the sphere x2+y2+z2=1a+1b+1c.x^2 +y^2 +z^2 =\frac{1}{a}+\frac{1}{b}+\frac{1}{c}.
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