The length of tangent from the point $(5, 1)$ to the circle ${x^2} + {y^2} + 6x - 4y - 3 = 0$, is
$81$
$29$
$7$
$21$
If the line $y = \sqrt 3 x + k$ touches the circle ${x^2} + {y^2} = 16$, then $k =$
Number of integral points interior to the circle $x^2 + y^2 = 10$ from which exactly one real tangent can be drawn to the curve $\sqrt {{{\left( {x + 5\sqrt 2 } \right)}^2} + {y^2}} \, - \sqrt {{{\left( {x - 5\sqrt 2 } \right)}^2} + {y^2}\,} \, = 10$ are (where integral point $(x, y)$ means $x, y \in I)$
Length of the tangent from $({x_1},{y_1})$ to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
The tangent at $P$, any point on the circle ${x^2} + {y^2} = 4$, meets the coordinate axes in $A$ and $B$, then
The number of tangents that can be drawn from $(0, 0)$ to the circle ${x^2} + {y^2} + 2x + 6y - 15 = 0$ is