Question

Find the angle between the line given by the
equation $\lambda y^2+(1-{\lambda }^2)xy-\lambda x^2=0$ is

• A. ${45}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${15}^o$

Answer 1

The correct option is C ${90}^o$

Pair of straight lines through origin.

$y=m_{1}x,y=m_{2}x$

$(y-m_{1}x)(y-m_{2}x)=0$

$y^2-(m_1+m_2)xy+m_1{m}_2{x}^2=0$

comparing with $\lambda y^2+(1-{\lambda }^2)xy-\lambda x^2=0$

$\frac{1}{\lambda }=-\frac{(m_1+m_2)}{(1-{\lambda }^2)}=\frac{m_1{m}_2}{-\lambda }$

$m_1+m_2=\frac{{\lambda }^2-1}{\lambda }{m}_1{m}_2=-1$

lines are having ${90}^o$ angle between them.

C is correct