If the line $x = 7$ touches the circle ${x^2} + {y^2} - 4x - 6y - 12 = 0$,then the coordinates of the point of contact are:

If $P(\frac{\pi}{4})$ and $Q(\frac{\pi}{3})$ are two points on the circle $x^2+y^2-2x-2y-1=0$,then the slope of the tangent to this circle which is parallel to the chord $PQ$ is

If $\theta$ is the acute angle between the curves $x^2+y^2=4$ and $y^2=3x$, then $\tan \theta=$

If the line $y = mx + c$ is a tangent to the circle $x^2 + y^2 = a^2$,then the point of contact is

If the tangent drawn 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

The angle between the tangents drawn from the origin $(0, 0)$ to the circle $(x - 7)^2 + (y + 1)^2 = 25$ is (in $^\circ$)