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Question

If ax+by+c=0 and lx+my+n=0 are asymptotes of a hyperbola, then


A
ambl
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B
am+blal+bm>4
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C
albm
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D
none of these
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Solution

The correct option is A ambl
Equation of a hyperbola whose asymptotes are ax+by+c=0 and b+my+n=0 can be written as (ax+by+c)(1x+my+n)=λ

i.e. alx2+(am+bl)xy+bmy2+(an+cl)x+(bn+cm)y+cnλ=0

which will represent a hyperbola if (am+bl2)2albm>0

i.e. (am+bl)24(am)(bl)>0
i.e. (ambl)2>0
i.e. ambl

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