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If the equation 6x^2-11xy-10y^2-19y+c=0 represents a pair of straight lines find their quarks. Also find the angle between the two lines.

If the equation 6x^2-11xy-10y^2-19y+c=0 represents a pair of straight lines find their quarks. Also find the angle between the two lines.

Grade:12

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
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harshita
13 Points
8 months ago
we are given the equation of staright line 6x2-11xy-10y2-19y+c=0
=> 6x2-11xy-10y2=19y-c
=> 6x2-15xy+4xy-10y2=19y-c
=> (3x+2y)(2x-5y)=19y-c
      straight line will be of the form 
      3x+2y+c1=0 and 2x-5y+c2=0
=>  2c1+3c2=0----------1
=>  2c2-5c1= -19
=>  c1c2=c
      from equation 1 and 2 we get;
      c1=3 and c2= -2
      c1c2=c= -6
      hence two lines will be 2x-5y-2=0 and 3x+2y+3=0
    

 

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