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In my textbook of Arihant publications it says:

If a conic represents an empty set then, ∆ not= 0 and h^2

I don't understand what is meant by an empty set represented by the conic and how this relation is derived??

J. W. Tanner
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Hritwik Raj
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    this seems incomplete. What did you mean by "$\Delta \neq 0$ and $h^2$"? In any case, a conic can certainly be empty, as in $x^2+y^2=-1$. – lulu Mar 07 '19 at 17:35
  • For any conic- ax^2 + 2hxy + by^2 + 2gx +2fy +c =0. ∆= abc+ 2fgh -af^2 - bg^2 - ch^2. ∆ regulates the nature of conic. If ∆= 0the equation represents pair of straight lines and if it is not it represents the conic section. – Hritwik Raj Mar 11 '19 at 14:00

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