A tangent to the circle ${x^2} + {y^2} = 5$at the point $(1,-2)$ the circle ${x^2} + {y^2} - 8x + 6y + 20 = 0$

The straight line $x + 2y = 1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A, B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is

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?

The equation of tangent to the circle ${x^2} + {y^2} = {a^2}$ parallel to $y = mx + c$ is

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

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