Question

Let there are two lines $2x+3y+\lambda =0$ and $\lambda x-3y-1=0$. If the origin lies in the obtuse angle then

• A. $\lambda =\frac{9}{2}$
• B. $-2<\lambda <0$
• C. $-2<\lambda <\frac{9}{2}$
• D. $Noneofthese$

Answer 1

The correct option is C $-2<\lambda <\frac{9}{2}$

$2x+3y+\lambda =0$

$y=\frac{-2}{3}x-\frac{\lambda }{3}$

$m_1=\frac{-2}{3}$

$\lambda x-3y=-1$

$y=\frac{\lambda }{3}x-\frac{1}{3}$

$m_2=\frac{\lambda }{3}$

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$.