Question

If a hyperbola passing through the origin has `3x-4y-1=0` and `4x-3y-6=0` as its asymptotes, then find the equation of its transvers and conjugate axes.

Answer 1

The axes of a hyperbola are the bisectors of the pair of asymptotes.
The tranverse axis is the bisector which contains the origin and is given
`(3x-4y-1)/(5)=+(4x-3y-6)/(5)`
`"or "x+y-5=0`
The conjugate axis is
`(3x-4y-1)/(5)=-(4x-3y-6)/(5)`
`"or "x-y-1=0`