According to the
question..........
$\begin{array}{l} Let,\, { m _{ 1\, } }& \, { m _{
2 } } \ sum\, of\, the\, slope:\, { m _{ 1 } }+{ m _{ 2 } }=\dfrac { { -2h } }{
b } ----(i) \ and,\, \ product\, of\, slope:{ m _{ 1 } }.\, { m _{ 2 }
}=\dfrac { a }{ b } -----(ii) \ Here, \ a{ x^{ 2 } }+2hxy+b{ y^{ 2 }
}=0.........(general\, equ\, of\, straight\, line.) \ cofficient\, of: \ a={
\sec ^{ 2 } }\theta -{ \sin ^{ 2 } }\theta \ h=-\tan
\theta \ b={ \sin ^{ 2 } }\theta \ Now,\, value\, put\, { {
into } } \ sum\, of\, the\, slope:\, { m _{ 1 } }+{ m _{ 2 } }=\dfrac { { -2h }
}{ b } ----(i) \ \Rightarrow { m _{ 1 } }+{ m _{ 2 } }=\dfrac { { -2(-tan\theta
) } }{ { { { \sin }^{ 2 } }\theta } } =\dfrac { { 2\sin
\theta \times 2 } }{ { 2{ { \sin }^{ 2 } }\theta \, .\, \cos
\theta } } =\dfrac { 4 }{ { 2sin\theta \cos \theta } } =\dfrac
{ 4 }{ { \sin 2\theta } } \ and, \ product\, of\, slope:{
m _{ 1 } }+{ m _{ 2 } }=\dfrac { a }{ b } -----(ii) \ \Rightarrow { m _{ 1 } }.\,
{ m _{ 2 } }=\dfrac { { { { \sec }^{ 2 } }\theta -{ { \sin
}^{ 2 } }\theta } }{ { { { \sin }^{ 2 } }\theta }
} =\dfrac { 1 }{ { { { \sin }^{ 2 } }\theta \, .\, { { \cos
}^{ 2 } }\theta } } -1\, \, \, \, \, \, \, \, \left[ { divide\,
by\, 4 } \right. \ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \,
\, \, \, =\dfrac { 4 }{ { 4{ { \sin }^{ 2 } }\theta \, .\, { {
\cos }^{ 2 } }\theta } } -1\, \, =\dfrac { 4 }{ { { {
(\sin 2\theta ) }^{ 2 } }\, } } -1\, \ \, \, \, Now,find\,
difference: \ \, \, \, \, \, \, \, \, \, { ({ m _{ 1 } }-{ m _{ 2 } })^{ 2 } }={
({ m _{ 1 } }+{ m _{ 2 } })^{ 2 } }-4{ m _{ 1 } }.\, { m _{ 2 } } \ \, \, \, \, \,
\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \,
\, \, \, ={ \left( { \dfrac { 4 }{ { \sin 2\theta } } }
\right) ^{ 2 } }-4\left( { \dfrac { 4 }{ { ({ { \sin }^{ 2 }
}2\theta )\, } } -1\, } \right) \ \, \, \, \, \, \, \, \, \,
\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, =\dfrac
{ { 16 } }{ { ({ { \sin }^{ 2 } }2\theta )\, } } -\, \dfrac {
{ 16 } }{ { ({ { \sin }^{ 2 } }2\theta )\, } } +4 \ \, \, \,
\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \Rightarrow \, \, { ({ m _{ 1 } }-{
m _{ 2 } })^{ 2 } }\, \, \, =4 \ \, \, \, \, \, \, \, \, \, \, \, \, \, \, \,
\, \, \, \, \Rightarrow \, ({ m _{ 1 } }-{ m _{ 2 } })=+\sqrt { 4 } =2 \ \, \,
\, \therefore \, \, \, the\, \, differece\, of\, slope\, \, is\, 2. \ So,\,
that\, the\, correct\, option\, is\, B.\, \, \, \, \, \, \, \, \, \, \, \, \,
\, \, \, \, \, \end{array}$