If the slope of one line of the pair of lines $2 x^2+h x y+6 y^2$ $=0$ is thrice the slone of the other line…
If the slope of one line of the pair of lines $2 x^2+h x y+6 y^2$ $=0$ is thrice the slone of the other line, then $\mathrm{h}=$
$\pm 16$
$\pm 9$
$\pm 18$
$\pm 8$
Solution
$2 x^2+h x y+6 y^2=0$
Comparing with $a x^2+2 h x y+b y^2=0$
$a=4, b=12$
Let $m_1$ and $m_2$ be the slopes
We know, $m_1 m_2=\frac{a}{b}=\frac{1}{3}$
Also $m_1=3 m_2 \Rightarrow 3 m_1^2=\frac{1}{3} \Rightarrow m_1= \pm \frac{1}{3}$
And $m_1+m_2=-\frac{2 h}{b} \Rightarrow 4 m_1=\frac{-2 h}{12} \Rightarrow h= \pm 8$