The directrix 3x-4y=18 is perpendicular to the axis of symmetry.
4y=3x-18, so the slope is ¾ and the slope of the perpendicular is -4/3, because 3/4×(-4/3)=-1, the condition for perpendicularity. The focus lies on the axis of symmetry so the equation of the axis of symmetry must pass through the focus, making the focus a point on this perpendicular:
y-5=-(4/3)(x+4), y-5=-4x/3-16/3, y=-4x/3-1/3, or 3y=-(4x+1), or 4x+3y=-1.