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

Options

A. 4
B. 3
C. 2
D. None of these

Answer

C

Explanation

Given, equation of lines `x^2(sec^2theta-sin^2theta)-2xytantheta+y^2sin^2theta=0` ...(i)
Let `m_1 and m_2` be the slopes of lines represented by Eq. (i)
Then , `m_1+m_2=(2tan theta)/(sin^2theta)`
and `m_1.m_2=(sec^2theta-sin^2theta)/(sin^2theta)`
Now , `m_1-m_2=sqrt((m_1+m_2)^2-4m_1m_2)`
`=sqrt((4tan^2theta)/(sin^4theta)-4((sec^2theta-sin^2theta)/(sin^2theta)))`
`=2sqrt((tan^2theta-sin^2thetasec^2theta+sin^4theta)/(sin^4theta))`
`=2sqrt((tan^2theta-tan^2theta+sin^4theta)/(sin^4theta))`
`therefore m_1-m_2=2`