Question

The condition that the slope of one of the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is twice that of the other is

• A. $h^2=ab$
• B. $2h^2=3ab$
• C. $8h^2=9ab$
• D. $4h^2=9ab$

Answer 1

Answer: (C)

$8h^2=9ab$

We know that ,

for $a{x}^2+2hxy+b{y}^2=0$

$m_1+m_2=\frac{-2h}{b}{m}_1{m}_2=\frac{a}{b}$

Let the Roots be $m,2m$

$2m\ast m=\frac{a}{b}2m+m=3m=\frac{-2h}{b}\Rightarrow m=\frac{-2h}{3b}$

So,

$\frac{a}{b}=2m^2\Rightarrow \frac{a}{b}=2(\frac{-2h}{3b}{)}^2\Rightarrow \frac{a}{b}=\frac{8h^2}{9b^2}\Rightarrow 8h^2=9ab$