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

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 $x - y - 5 = 0$

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

$\frac{- 3 x + 4 y + 1}{\sqrt{9 + 16}} = \frac{- 4 x + 3 y + 6}{\sqrt{16 + 9}}$

and,

$\frac{- 3 x + 4 y + 1}{\sqrt{9 + 16}} = - \frac{- 4 x + 3 y + 6}{\sqrt{16 + 9}}$

$\Rightarrow$ $x + y - 5 = 0$ and $x - y - 1 = 0 .$

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

Solution:

Related content