Question

The length of the transverse axis of the hyperbola $9\,x^{2}-16\,y^{2}-18\,x-32\,y-151=0$ is

Answer 1

The equation of given hyperbola is
$9x^{2}-16y^{2}-18x-32y-151=0$
We can simplify it as
$9x^{2}-18x+9-16y^{2}-32y-16-151+7=0$
$\Rightarrow 9\left(x - 1\right)^{2}-16\left(y + 1\right)^{2}=144\,$
$\Rightarrow \frac{\left(x - 1\right)^{2}}{16}-\frac{\left(y + 1\right)^{2}}{9}=1\,$
Length of the transverse axis is $2\,a=8.$