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.

Question

Deepak Kumar Shringi · Answer

harshita · Answer

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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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.

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