The lines $y - y_1 = m (x - x_1) \pm a \,\sqrt {1\,\, + \,\,{m^2}} $ are tangents to the same circle . The radius of the circle is :

The normal to the circle ${x^2} + {y^2} - 3x - 6y - 10 = 0$at the point $(-3, 4)$, is

If the line $y = \sqrt 3 x + k$ touches the circle ${x^2} + {y^2} = 16$, then $k =$

The equations of the tangents to the circle ${x^2} + {y^2} = {a^2}$ parallel to the line $\sqrt 3 x + y + 3 = 0$ are

Line $y = x + a\sqrt 2 $ is a tangent to the circle ${x^2} + {y^2} = {a^2}$ at

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2 + y^2 + 4x -6y = 12$ externally at the point $(1, -1)$, then the radius of $C$ is