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 straight line $x+2y=1$ cuts the $X$-axis at $A$ and the $Y$-axis at $B$. $A$ circle is drawn through $A, B$ and the origin $O(0,0)$. The sum of the perpendicular distances from $A$ and $B$ to the tangent drawn at the origin to the circle $S$ is:

If $\theta$ is the angle between the pair of tangents drawn from a point $P(x_1, y_1)$ to the circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$,then which of the following is true?

The condition that the line $x \cos \alpha + y \sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is

The equation of the tangent to the circle $x^2 + y^2 = a^2$ which makes a triangle of area $a^2$ with the coordinate axes is:

If the line $(x + g) \cos \theta + (y + f) \sin \theta = k$ is tangent to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$,then: