Question

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

• A. $x+y=5$ and $x-y=5$
• B. $x+y=5$ and $x-y=1$
• C. $x-y=1$ and $x+y=5$
• D. $x-y=5$ and $x+y=5$

Answer 1

The correct option is B $x+y=5$ and $x-y=1$

Axes of hyperbola are bisectors of pair of asymptotes.
Transverse axis is the bisector which contains the origin and is given by
$\frac{3x-4y-1}{5}=+\frac{4x-3y-6}{5}$
$\Rightarrow x+y=5$

And conjugate axis is,
$\frac{3x-4y-1}{5}=-\frac{4x-3y-6}{5}$
$\Rightarrow x-y=1$