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

If the line $y$ $\cos \alpha = x\sin \alpha + a\cos \alpha $ be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then

If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle, then the radius of the circle is

If the centre of a circle is $(-6, 8)$ and it passes through the origin, then equation to its tangent at the origin, is

Tangents are drawn from $(4, 4) $ to the circle $x^2 + y^2 - 2x - 2y - 7 = 0$ to meet the circle at $A$ and $B$. The length of the chord $AB $ is

If the point $(1, 4)$ lies inside the circle $x^2 + y^2-6x - 10y + p = 0$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of $p$ is the interval