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  • If the slope of the lines represented by 6x²+ 2hxy+ y² = 0 are in ratio 1: 2 then h = ?

If the slope of the lines represented by 6x²+ 2hxy+ y² = 0 are in ratio 1: 2 then h = ?

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Solution: We have ,

\ 6x^2 +2hxy+y^2  And \ m1/m2=1/2

We know ,let the equation of the pair of straight line 

\Rightarrow ax^2+2hxy+by^2   

Therefore , (m1+m2) =(-2h/b) and m1× m2 =a/b

Hence ,  \ Rightarrow (m+2m)=-2h \\Rightarrow (m imes 2m)=6\ \Rightarrow m=sqrt3

\Rightarrow (m+2m)=-2h \ \Rightarrow 3m=-2h\ \Rightarrow h=3m/-2\ \Rightarrow h=-3sqrt3/2

 

Posted by

Deependra Verma

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