If the slope of the lines represented by 6xÂ²+ 2hxy+ yÂ² = 0 are in ratio 1: 2 then h = ?

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 ,  $\\ \Rightarrow (m+2m)=-2h \\\\\Rightarrow (m\times 2m)=6\\ \\\Rightarrow m=\sqrt{3}$

$\\\Rightarrow (m+2m)=-2h \\ \\\Rightarrow 3m=-2h\\ \\\Rightarrow h=3m/-2\\ \\\Rightarrow h=-3\sqrt{3}/2$

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