Angle between Pair of Tangents

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. $\frac{\pi }{2}$
4. $\frac{\pi }{6}$

Q.

If $\frac{x}{\alpha }+\frac{y}{\beta }=1$ touches the circles $x^2+y^2=a^2$, then point $\left(\frac{1}{\alpha },\frac{1}{\beta }\right)$ lies on

1. Straight line

2. Circle

3. Parabola

4. Ellipse