Difference of slopes of the lines represented by the equation `x^2(sec^2 theta - sin ^2 theta) -2xytan theta + y^2 sin^2 theta=0` is(A) `4`(B) `3`(C) `2`(D) None of these

Difference of slopes of the lines represented by the equation `x^2(sec

1.	Difference of slopes of the lines represented by the equation `x^2(sec^2 theta - sin ^2 theta) -2xytan theta + y^2 sin^2 theta=0` is(A) `4`(B) `3`(C) `2`(D) None of these
Answer» Let we have below two lines that represent the given equation. `y-m_1x = 0` and `y-m_2x=0` Combined equation of these two lines will be, `(y-m_1x)(y-m_2x) = 0` `y^2-(m_1+m_2)xy+m_1m_2x^2=0->(1)` Now, the given equation is, `x^2(sec^2theta -sin^2theta)-2xytantheta+y^2sin^2theta = 0` `=> x^2((sec^2theta -sin^2theta)/sin^2theta)-2tantheta/sin^2thetaxy+y^2=0` `=>y^2-2secthetacosecthetaxy+(sec^2thetacosec^2theta-1)x^2` Comparing this with the given equation (1), `m_1+m_2 = 2secthetacosectheta` `m_1m_2 = sec^2thetacosec^2theta-1` `(m_1-m_2)^2 = (m_1+m_2)^2-4m_1m_2` `=>(m_1-m_2)^2 = 4sec^2thetacosec^2theta-4sec^2thetacosec^2theta+4` `=>(m_1-m_2)^2 = 4` `\|m_1-m_2\| = 2`

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Difference of slopes of the lines represented by the equation `x^2(sec^2 theta - sin ^2 theta) -2xytan theta + y^2 sin^2 theta=0` is(A) `4`(B) `3`(C) `2`(D) None of these

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