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  4. If the slopes of the lines 3 x2+2 h x y+4 y2=0 are in the ratio 3: 1 then hequals

Q. If the slopes of the lines $3 x^{2}+2 h x y+4 y^{2}=0$ are in the ratio $3: 1$ then hequals

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Solution:

$m _{1}+ m _{2}=\frac{-2 h }{4}$........(1)
$m _{1} m _{2}=\frac{3}{4}$..........(2)
$m _{1}=3 m _{2}$ (By data), From (1) $3 m _{2}=\frac{-2 h }{4}$
and $m _{2}= \frac{-2 h }{12}=-\frac{h}{6} ;$
From (2) $3 m _{2}^{2}=\frac{3}{4} $
$ \Rightarrow m _{2}=\pm \frac{1}{2} ; m _{1}=4$
or $-4$

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