☼ Pairs of  Lines  :

 (i) The equation  ax² + 2 hxy + by²  =  0  represents a pair of  lines passing through the origin if  h²  ab.

The above equations for pair of  lines are called the general homogeneous quadratic equation.

 (ii) The angle between two lines given  by  ax² + 2 hxy + by²  =  0  is :

   =  tan^{– 1}  

 (iii) Two lines represented by  ax² + 2 hxy + by²  =  0  will :

  Coincide, if  h² = ab.

   be perpendicular,  if  a + b  =  0.

 (iv) The equation of  the bisectors of  the angles between the lines  ax² + 2 hxy + by²  =  0  are; 

 (v) The equation  ax² + 2 hxy + by² + 2 gx + 2 fy + c  =  0   will  represent  a  pair  of  lines [ intersecting each other at P (x, y) ],  if  abc + 2 fgh – af² – bg² – ch²  =  0.

The above equations for pair of  lines are called the general quadratic equation.

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