If a hyperbola passing through the origin has 3x−4y−1=0 and 4x−3y−6=0 as its asymptotes, then the equations of its transverse and conjugate axes, are

If a hyperbola passing through the origin has 3x4y1=0 and 4x3y6=0 as its asymptotes, then the equations of its transverse and conjugate axes, are

  1. A

    xy5=0 and x+y+1=0

  2. B

    xy=0 and x+y+5=0

  3. C

    x+y5=0 and xy1=0

  4. D

    x+y1=0 and xy5=0

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    Solution:

    The transverse axis is the bisector of the angle between asymptotes containing the origin and the conjugate axis is the other bisector. So, their equations are given by

    3x+4y+19+16=4x+3y+616+9

    and,

    3x+4y+19+16=4x+3y+616+9

     x+y5=0 and xy1=0

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