Question

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

A
45o
B
60o
C
90o
D
15o

Solution

## 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 $$\lambda y^2 + (1 - \lambda^2) xy - \lambda x^2 = 0$$$$\dfrac{1}{\lambda} = -\dfrac{(m_1 + m_2)}{(1 - \lambda^2)} = \dfrac{m_1m_2}{-\lambda}$$$$m_1 + m_2 = \dfrac{\lambda^2 - 1}{\lambda} \,\, m_1 m_2 = -1$$lines are having $$90^o$$ angle between them.C is correctMaths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More