Centre of Hyperbola

Q. If the pair of straight lines $x^2-y^2+6x+4y+5=0$ represents transverse and conjugate axes of the hyperbola and centre of hyberbola is $(\alpha ,\beta )$, then value of $\beta -\alpha$ is

Q.

The equation of the hyperbola whose centre is (5, 2), vertex is (9, 2) and the length of conjugate axis is 6 is

1. $\frac{(x-5{)}^2}{16}-\frac{(y-2{)}^2}{9}=-1$

2. $\frac{(x-2{)}^2}{5}-\frac{(y-2{)}^2}{9}=1$

3. $\frac{(x+2{)}^2}{7}-\frac{(y+2{)}^2}{9}=1$

4. $\frac{(x-2{)}^2}{17}+\frac{(y-2{)}^2}{19}=1$

Q.

The centre of the hyperbola 2xy+3x+4y+1=0 is

1. $(\frac{-3}{2},-2)$

2. $(-2,\frac{-3}{2})$

3. $(2,\frac{3}{2})$

4. $(\frac{3}{2},2)$