Directrix of Hyperbola

Q. If $a,b,c$ are in $A.P$, the straight line $ax+by+c=0$, passes through a fixed point which lie on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1,$ then eccentricity of hyperbola is

Q.

In a hyperbola the distance between the foci is 2 and the distance between directrices is 1 Its eccentricity is

1. $\sqrt{3}$

2. $\frac{3}{2}$

3. $\sqrt{2}$

4. $\frac{5}{2}$

Q.

In a hyperbola e = $\frac{9}{4}$ and the distance between the directrices is 3. Then the length of Transverse axis is

1. $\frac{27}{2}$

2. $\frac{27}{8}$

3. $\frac{27}{4}$

4. $\frac{17}{4}$