Angle between pair of tangents

Q. The angle between the tangents from $(\alpha ,\beta )$ to the circle $x^2+y^2=a^2$, is

1. $ta{n}^{-1}\frac{a}{\sqrt{{\alpha }^2+{\beta }^2-a^2}}$
2. $2ta{n}^{-1}\frac{a}{\sqrt{{\alpha }^2+{\beta }^2-a^2}}$
3. $ta{n}^{-1}\frac{\sqrt{{\alpha }^2+{\beta }^2-a^2}}{a}$
4. $Noneofthese$

Q.

The angle between a pair of tangents drawn from a point P to the circle $x^2+y^2+4x-6y+9si{n}^2\alpha +13co{s}^2\alpha =0is2\alpha .$ The equation of the locus of the point P is

1. $x^2+y^2+4x-6y-9=0$

2. $x^2+y^2+4x-6y-4=0$

3. $x^2+y^2+4x-6y+4=0$

4. $x^2+y^2+4x-6y+9=0$

Q. The angle between the two tangents from the origin to the circle $(x-7{)}^2+(y+1{)}^2=25$ is

1. 0
2. $\frac{\pi }{3}$
3. $\frac{\pi }{6}$
4. $\frac{\pi }{2}$