IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

ashish_banga

If the two pairs of lines ${x}^{2} - 2mxy -{y}^{2} = 0$ and ${x}^{2} - 2 nxy - {y}^{2} = 0$ are such that one of them represents the bisectors of the angles between the other, then find the relation between n and m

Answer: nm+1 = 0

Aatish

Hey buddy,,,,,,,,

well.....simple application.......

for any homogeneous equation of pair of lines passing through origin........

$a{x}^{2} + 2hxy + b{y}^{2} = 0$

joint equation of the pair of angle bisectors is given by........

$\frac{{x}^{2} - {y}^{2}}{a-b} = \frac{xy}{h}$

here we have.........

a = 1, b = -1, h = -m {considering first equation}

then joint equation of the pair of angle bisectors comes out to be,,,,,,,

${x}^{2}+\frac{2xy}{m}-{y}^{2} = 0$

Now compare it with the second equation.......and u will get the answer,,,,,,

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