Focii of Hyperbola

Q.

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

1. 5/2

2. 

3. 3/2

4. 

Q. For the hyperbola $\frac{(3x-4y-12{)}^2}{100}-\frac{(4x+3y-12{)}^2}{225}=1$

1. coordinates of center is$(\frac{84}{25},\frac{-12}{25})$
2. coordinates of center is $(\frac{12}{25},\frac{84}{25})$
3. coordinates of foci is $(\frac{84\pm 100\sqrt{13}}{25},\frac{-12\mp 75\sqrt{13}}{25})$
4. coordinates of foci is $(\frac{84\pm 15\sqrt{13}}{25},\frac{-12\mp 20\sqrt{13}}{25})$

Q.

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

1. $x^{2}cose{c}^2\theta -y^{2}se{c}^2\theta =1$

2. $x^{2}se{c}^2\theta -y^{2}cose{c}^2\theta =1$

3. $x^{2}si{n}^2\theta -y^{2}co{s}^2\theta =1$

4. $x^{2}co{s}^2\theta -y^{2}si{n}^2\theta =1$

Q.

If P is a point on the hyperbola $16x^2-9y^2=144$ whose foci are $S_{1}and{S}_2,thenP{S}_1\sim P{S}_2=$

1. 4

2. 6

3. 8

4. 12