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If the pairs of straight lines ax^2+2hxy...

If the pairs of straight lines `ax^2+2hxy-ay^2=0` and 'bx^2+2gxy-by^2=0` be such that each bisects the angles between the other , then

A

`hg+ab=0`

B

`ah+hb=0`

C

`h^2-ab=0`

D

`ag+bh=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Since , each pair of lines bisects the angles between the other. So , the equation of bisectors of the angles between the lines is given by `ax^2+2hxy-ay^2=0` is `bx^2+2gxy-by^2=0`....(i)
The equation of bisectors of the angles between the lines given by `ax^2+2hxy-ay^2=0` is `(x^2-y^2)/(a-(-a))=(xy)/(h)`
`rArr hx^2-2axy-hy^2=0` .........(ii)
Since , Eqs. (i) and (ii) represent the same pair of straight lines.
`therefore (b)/(h)=(g)/(-a)=(-b)/(-h)`
`rArr ab=-ghrArr ab+gh=0`
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