Question

Assertion :The combined equation of $l_1,l_2$ is given by $5x^2+24xy+y^2=0$ & that of $m_1,m_2$ is given by $7x^2+36xy+y^2=0$. If the angle between $l_1,m_2$ is $\theta$ then the angle between $l_2,m_1$ is also $\theta$. Reason: If the pair of lines $l_1{l}_2=0$ & $m_1{m}_2=0$ are equally inclined, then angle between $l_1{m}_2$ is equal to the angle between $l_2{m}_1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given eq of pair of bisector of

$5x^2+24xy+y^2=0$ is

$\frac{x^2-y^2}{5-1}=\frac{xy}{12}$ or $\frac{x^2-y^2}{1}=\frac{xy}{3}$-----(1)

and eq of pair of bisector of $7x^2+36xy+y^2=0$ is given by

$\frac{x^2-y^2}{7-1}=\frac{xy}{18}$ or $\frac{x^2-y^2}{1}=\frac{xy}{3}$-----(2)

$\therefore$ from eq (1) and (2)

pair of bisectors of given lines are coincident

$\therefore$ Angle between $l_1,m_2$ is same as the angle between $l_2,m_1$