Necessary and Sufficient Conditions for the General Second Degree Equation
$$Ax^2+2Hxy+By^2+2Gx+2Fy+C=0$$
 to Represent Pair of Straight Lines:

$$\Delta =\begin{vmatrix} A &  H &G\\  H& B & F\\  G& F& C \end{vmatrix} =0$$


Case 1 :if $$H^2 > AB$$ Then they are Intersecting pair of Straight Lines

Case 2: if $$H^2 = AB$$ Then they are pair of Parallel Straight Lines

Case 3: if $$H^2 < AB$$ Then they Represent a Point in a Plane