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?
$3 x-4 y-24=0$
$3 x+4 y-6=0$
$4 x+3 y-8=0$
$4 x-3 y+17=0$
The line $x\cos \alpha + y\sin \alpha = p$will be a tangent to the circle ${x^2} + {y^2} - 2ax\cos \alpha - 2ay\sin \alpha = 0$, if $p = $
If the tangents drawn at the point $O (0,0)$ and $P (1+\sqrt{5}, 2)$ on the circle $x ^{2}+ y ^{2}-2 x -4 y =0$ intersect at the point $Q$, then the area of the triangle $OPQ$ is equal to
If the line $x = k$ touches the circle ${x^2} + {y^2} = 9$, then the value of $k$ is
The angle between the tangents to the circle ${x^2} + {y^2} = 169$ at the points $(5, 12) $ and $(12, -5)$ is ............. $^o$
The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-