Directrix of Hyperbola

Q.

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

1. 27/2

2. 27/8

3. 27/4

4. 17/4

Q.

From a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ lines are drawn to focus S

and directrix perpendicular to it as shown.Then,

1. 

2. 

3. 

4. 

Q.

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

1. 

2. 3/2

3. 

4. 5/2

Q. If the distance between the foci and the distance between two directrices of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are in the ratio $3:2$, then $b:a$ is

1. $\sqrt{3}:\sqrt{2}$
2. $1:2$
3. $2:1$
4. $1:\sqrt{2}$

Q. A hyperbola having the transverse axis of length $2\sin \theta$ unit, is confocal with the ellipse $3x^2+4y^2=12$, then its equation is

1. $x^2{\text{cosec}}^2\theta -y^2{\sec }^2\theta =1$
2. $x^2{\sec }^2\theta -y^2{\text{cosec}}^2\theta =1$
3. $x^2{\cos }^2\theta -y^2{\sin }^2\theta =1$
4. $x^2{\sin }^2\theta -y^2{\cos }^2\theta =1$

Q. The ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and hyperbola $\frac{x^2}{A^2}-\frac{y^2}{B^2}=1$ are having a same foci and length of minor axis of ellipse is same as the conjugate axis of the hyperbola. If $e_1$ & $e_2$ are the eccentricities of ellipse and hyperbola respectively, then the value of $\frac{1}{e_1^2}+\frac{1}{e_2^2}$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q. If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2\sqrt{3})$ is $5x=4\sqrt{5}$ and its eccentricity is $e$, then :

1. $4e^4-24e^2+27=0$
2. $4e^4+8e^2-35=0$
3. $4e^4-24e^2+35=0$
4. $4e^4-12e^2-27=0$

Q. The locus of the point of intersection of the lines $bxt-ayt=ab$ and $bx+ay=abt$, $t$ being parameter is

1. an ellipse with equation $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
2. a hyperbola with equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
3. a hyperbola with equation $\frac{x^2}{b^2}-\frac{y^2}{a^2}=1$
4. an ellipse with equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

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. The foci of the hyperbola are $S(5,6),S^{\prime }(-3,-2)$. If its eccentricity is $2$, then the equation of its directrix corresponding to focus $S$ is

1. $x+y-3=0$
2. $x+y-5=0$
3. $x+y-1=0$
4. $x+y-7=0$