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Difference of slopes of the lines repres...

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

Text Solution

Verified by Experts

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`
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