Question

If the combined equation of asymptotes of the hyperbola $xy=3x-4y+16$ is $xy=3x-4y+k$ , then the value of $k$ is equal to

Answer 1

$xy-3x+4y-16=0$
$x\left(y - 3\right)+4\left(y - 3\right)-4=0$
$\left(x + 4\right)\left(y - 3\right)=4$
Its asymptotes are $x+4=0\&y-3=0$
The combined equation will be
$\left(x + 4\right)\left(y - 3\right)=4$
$\Rightarrow xy=3x-4y+12$