## Thursday, 18 April 2013

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