The equation of the pair of tangents at $(0,1)$ to the circle $x^{2}+y^{2}-2x-6y+6=0$ is

If the circles $x^2 + y^2 + 2ax + cy + a = 0$ and $x^2 + y^2 - 3ax + dy - 1 = 0$ intersect in two distinct points $P$ and $Q$,then the line $5x + by - a = 0$ passes through $P$ and $Q$ for

If the point of intersection of the tangents drawn at the points where the line $5x + y + 1 = 0$ cuts the circle $x^2 + y^2 - 2x - 6y - 8 = 0$ is $(a, b)$,then $5a + b =$

If the circles $x^2 + y^2 + 2ax + cy + a = 0$ and $x^2 + y^2 - 3ax + dy - 1 = 0$ intersect at two distinct points $P$ and $Q$,then for what value of $a$ does the line $5x + 6y - a = 0$ pass through points $P$ and $Q$?

Tangents are drawn from $(4, 4)$ to the circle $x^2 + y^2 - 2x - 2y - 7 = 0$ to meet the circle at $A$ and $B$. The length of the chord $AB$ is

If $OA$ and $OB$ are the tangents to the circle $x^2 + y^2 - 6x - 8y + 21 = 0$ drawn from the origin $O$,then $AB =$