If the line $y = \sqrt 3 x + k$ touches the circle ${x^2} + {y^2} = 16$, then $k =$
$0$
$2$
$4$
$8$
(d) $k = \pm 4\sqrt {1 + 3} = \pm 8$ .
The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^{2}$ at the point $(2,4)$ is
The equation to the tangents to the circle ${x^2} + {y^2} = 4$, which are parallel to $x + 2y + 3 = 0$, are
The gradient of the normal at the point $(-2, -3)$ on the circle ${x^2} + {y^2} + 2x + 4y + 3 = 0$ is
If the tangent at the point $P$ on the circle ${x^2} + {y^2} + 6x + 6y = 2$ meets the straight line $5x – 2y + 6 = 0$ at a point $Q$ on the $y$- axis, then the length of $PQ$ is
If the lines $3x – 4y + 4 = 0$ and $6x – 8y – 7 = 0$ are tangents to a circle, then the radius of the circle is
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