The value of $c$, for which the line $y = 2x + c$ is a tangent to the circle ${x^2} + {y^2} = 16$, is
$ - 16\sqrt 5 $
$20$
$4\sqrt 5 $
$16\sqrt 5 $
If $2x - 4y = 9$ and $6x - 12y + 7 = 0$ are the tangents of same circle, then its radius will be
Let $PQ$ and $RS$ be tangents at the extremeties of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle, then $2r$ equals
A circle touches the $y$ -axis at the point $(0,4)$ and passes through the point $(2,0) .$ Which of the following lines is not a tangent to this circle?
If the line $3x -4y -k = 0 (k > 0)$ touches the circle $x^2 + y^2 -4x -8y -5 = 0$ at $(a, b)$ then $k + a + b$ is equal to :-
The equations of the tangents to the circle ${x^2} + {y^2} = 36$ which are inclined at an angle of ${45^o}$ to the $x$-axis are