One of the focii of hyperbola is origin and the corresponding directrix is $3x + 4y + 1=0$. The eccentricity of the hyperbola is $\sqrt{5}$. The equation to the hyperbola is :

Question

( A ) $8x^2 + 9y^2 + 24xy + 6x + 6y + 1 =0$
( B ) $8x^2 + 9y^2 + 24xy + 6x + 8y + 1 =0$
( C ) $8x^2 + 15y^2 + 24xy + 6x + 8y + 1 =0$
( D ) $8x^2 + 9y^2 - 24xy + 6x + 8y + 1 =0$