Centre of Hyperbola

Q. For the given hyperbola $9x^2-16y^2+18x+32y-151=0$, which of the following options is/are true:

1. Centre of hyperbola is $(-1,1)$.
2. Length of transverse axis is $8$ units.
3. Length of conjugate axis is $6$ units.
4. Eccentricity of hyperbola is $3$.

Q.

The latusrectum of a hyperbola subtends a right angle at its centre, then its e =

1. $\frac{\sqrt{5}-1}{2}$

2. $\frac{\sqrt{5}+1}{2}$

3. $\frac{\sqrt{5}+2}{2}$

4. $\frac{\sqrt{5}+1}{3}$

Q. The asymptotes of a hyperbola have center at the point $(1,2)$ and are parallel to the lines $2x+3y=0$ and $3x+2y=0$. If the hyperbola passes through the point $(5,3)$, then its equation is

1. $(3x+2y-8)(2x+3y-7)-156=0$
2. $(2x+3y-8)(3x+2y-7)-154=0$
3. $(2x+3y-7)(3x+2y+8)-348=0$
4. $(3x+2y-8)(2x+3y+7)-338=0$

Q. The asymptotes of a hyperbola have center at the point $(1,2)$ and are parallel to the lines $2x+3y=0$ and $3x+2y=0$. If the hyperbola passes through the point $(5,3)$, then its equation is

1. $(3x+2y-8)(2x+3y-7)-156=0$
2. $(2x+3y-8)(3x+2y-7)-154=0$
3. $(2x+3y-7)(3x+2y+8)-348=0$
4. $(3x+2y-8)(2x+3y+7)-338=0$