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.
A. `x-y-5=0` and `x+y+1=0`
B. `x-y=0` and `x+y+5=0`
C. `x-y-5=0` and `x-y-1=0`
D. `x+y-1=0` and `x-y-5=0`

Answer 1

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+1)/(sqrt(9+16))=(-4x+3y+6)/(sqrt(16+9))`
and,
`(-3x+4y+1)/(sqrt(9+16))=(-4x+3y+6)/(sqrt(16+9))`
or, `x+y-5=0` and `x-y-1=0`