Empty or a Single point on a 2nd degree curve condition

Question

Is it true that if $\Delta \neq 0$ and $h^2 < ab$ we can have either empty points on the curve $ax^2 + by^2 + 2hxy + 2gx + 2fy + c= 0$ or the ellipse ? I know that in case of $\Delta = 0$ $h^2 < ab$ would represent a single point but how do we derive these conditions for single and empty points ? $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 $