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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

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