Putnam 1938 B6

13. Find the shortest distance between the plane $A x+B y+C z+1=0$ and the ellipsoid $x^{2} / a^{2}+y^{2} / b^{2}+z^{2} / c^{2}=1$. (For brevity, let $$\left.h=1 / \sqrt{A^{2}+B^{2}+C^{2}} \text { and } m=\sqrt{a^{2} A^{2}+b^{2} B^{2}+c^{2} C^{2}} .\right)$$

State algebraically the condition that the plane shall lie outside the ellipsoid.