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The lines y = mx bisects the angle betwe...

The lines `y = mx` bisects the angle between the lines `ax^(2) +2hxy +by^(2) = 0` if

A

`h(1+m^(2)) = m(a+b)`

B

`h(1-m^(2))=m(a-b)`

C

`h(1+m^(2))=m(a-b)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of pair of bisectors of angles between lines `ax^(2) +2hxy +by^(2) =0` is
`(x^(2)-y^(2))/(xy) =(a-b)/(h)`
`rArr h(x^(2)-y^(2)) =(a-b) xy` (i)
But `y = mx` is one of these lines, then it will satisfy it. Substituting `y = mx` in (i)
`h(x^(2)-m^(2)x^(2)) =(a-b) x.mx`
Dividing by `x^(2)`, we get `h (1-m^(2)) =m(a-b)`.
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