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  • The equation of a line passing through the centre of a rectangular hyperbola is

The equation of a line passing through the centre of a rectangular hyperbola is \mathrm{ x-y-1=0 }. if one of its asymptotes is \mathrm{ 3 x-4 y-6=0 }, the equation of the other asymptote is 

Option: 1

\mathrm{4 x+3 y+17=0}


Option: 2

\mathrm{4 x-3 y+17=0}


Option: 3

\mathrm{-4 x+3 y+1=0}


Option: 4

\mathrm{4 x+3 y+17=0}


Answers (1)

best_answer

We know that asymptotes of rectangular hyperbola are mutually perpendicular, thus other asymptote should be \mathrm{4 x+3 y+\lambda=0}. Intersection point of asymptotes is also the centre of the hyperbola.Hence intersection point of \mathrm{4 x+3 y+\lambda=0} and \mathrm{3 x-4 y-6=0} should lie on the line \mathrm{x-y-1=0}
using it \mathrm{\lambda} can be easily obtained.
Hence (d) is the correct answer.

Posted by

Suraj Bhandari

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