Discussion Forum

1)

If the slope of one of the lines given by ax²+2hxy+by² =0 is  two times the other, then

 

Answer:

Option A

Explanation:

 We have . ax²+2hxy+by²=0

 Let slope of one line is m

$\therefore$ Slope  of another line is 2m,

 We know that,

$m_{1}+m_{2}=-\frac{2h}{b}$

 and    $m_{1}m_{2}=\frac{a}{b}$

$\therefore$    $m+2m=-\frac{2h}{b}$

 $\Rightarrow$    $3m=-\frac{2h}{b}$  ......(i)

  and   $m(2m)=\frac{a}{b}$

 $\Rightarrow$     $2m^{2}=\frac{a}{b}$  ......(ii)

 On eliminating  m, we get

$2\left(\frac{-2h}{3b}\right)^{2}=\frac{a}{b}$

 $\Rightarrow$       $8h^{2}=9ab$