At which point on the $y$-axis is the line $x = 0$ a tangent to the circle $x^2 + y^2 - 2x - 6y + 9 = 0$?

If $O$ is the origin and $OP$,$OQ$ are tangents to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$,the circumcentre of the triangle $OPQ$ is

The equations of the tangents to the circle $x^2 + y^2 = 36$ which are inclined at an angle of $45^\circ$ to the $x$-axis are

If $y = c$ is a tangent to the circle $x^2 + y^2 - 2x + 2y - 2 = 0$ at the point $(1, 1)$,then the value of $c$ is:

The slope of a common tangent to the circles $x^2+y^2=16$ and $(x-9)^2+y^2=16$ is

The equation of the circle which touches the circle ${x^2 + y^2 - 6x + 6y + 17 = 0}$ externally and to which the lines ${x^2 - 3xy - 3x + 9y = 0}$ are normals,is