If the tangent at a point $P$ on the circle $x^2 + y^2 + 6x + 6y = 2$ meets the line $5x - 2y + 6 = 0$ at a point $Q$ on the $y$-axis,then the length of $PQ$ is . . . . .

Two tangents are drawn from a point $P$ to the circle $x^{2}+y^{2}-2x-4y+4=0$,such that the angle between these tangents is $\tan^{-1}\left(\frac{12}{5}\right)$,where $\tan^{-1}\left(\frac{12}{5}\right) \in (0, \pi)$. If the centre of the circle is denoted by $C$ and these tangents touch the circle at points $A$ and $B$,then the ratio of the areas of $\Delta PAB$ and $\Delta CAB$ is:

If $y=3x$ is a tangent to a circle with centre $(1,1)$,then the other tangent drawn through $(0,0)$ to the circle is

The angle between the tangents to the circle $x^2+y^2=25$ from the point $(1,7)$ is

The equations of the normals to the circle $x^2 + y^2 - 8x - 2y + 12 = 0$ at the points whose ordinate is $-1$ are:

The equations of the tangents to the circle $x^2+y^2=4$ drawn from the point $(4,0)$ are