The equation $9x^2 - 16y^2 -18x +32y-151=0$ represents a hyperbola . We have to find the equation of its directrix.
I simplified the equation and got : $$(3x-1)^2 -(4y-1)^2 = 151$$
And found that its center is $(\frac{1}{3},\frac{1}{4})$ .
But I am not getting how to find the equation of the directrix . For a standard hyperbola it is $x = \frac{a}{e}$ where $e$ is the eccentricity.
Once you have rewritten your equation as $$ {(x-x_0)^2\over a^2}-{(y-y_0)^2\over b^2}=1, $$ then the equation of a directrix is $x=x_0+a/e$, where $e=\sqrt{1+b^2/a^2}$.