PAIR OF STRAIGHT LINES

Are you already tensed by knowing that you are hardly left with two more months of preparation..? Now, its the time for you to give up your old practice methods and to make a perfect move..!!

Whenever you start any topic and learn it, make sure you note all the important formulae and shortcuts to make your revision more effective.

Here are few such tips on the topic Pair of Straight Lines.

  ü  Joint equation of the straight lines,   is 

  ü  If a,b,h are real then is called a homogenous equation of degree 2 

  ü  If a,b,h are not all 0 then the equation represents straight lines iff

  ü  If,lines are coincident.

  ü  If then we can writeso that

  ü  If H=0 represents a pair of straight lines and b is not equal to zero, if m1, m2  are slopes of lines.          Then 

              

          , .

  ü  The equation to the pair of lines passing through origin and perpendicular to pair of lines  is  is .

*** The product of perpendicular let fall from the point (x1, y1) upon the lines is  is .

**** Angle between pair of lines   is 

 And .

*** If the  lines are coincident then 

     

     

      If  the lines are perpendicular then 

   

 

 

*** Bisectors of the Angle between the lines by a Homogenous equation

ü  The joint equation of the bisectors of the angles between the lines represented by the equation  is .

**** The necessary and sufficient condition forto represent a pair of straight lines is that

 and .

**** Equations of bisectors:

** The equations of the bisectors of the angles between the lines represented byare given by .

Where (x1, y1) is the point of intersection of lines represented by given equations.

*** If   represents a pair of parallel straight lines then and distance between those parallel lines is

** If the equation  represent pair of straight lines then they intersect at point .

 **** if the equation  represents two straight lines then the product of perpendicular drawn from origin to these lines is 

.

** Area formed by lines represented  and axis of x is 

**** Lines joining origin to the point of intersection of curve:

The combined equation of the straight lines joining the origin to the points of intersection of a second degree curve   and a straight line  is  is 

** Area of triangle formed by=0 and  is is