If $(2, a)$ does not lie outside the circles $x^2+y^2=13$ and $x^2+y^2+x-2y=14$,then $a$ lies in

If the ratio of the lengths of tangents drawn from the point $(f, g)$ to the circles $x^2 + y^2 = 6$ and $x^2 + y^2 + 3x + 3y = 0$ is $2 : 1$,then:

Let $P(a, b)$ be a point on the parabola $y^2 = 8x$ such that the tangent at $P$ passes through the centre of the circle $x^2 + y^2 - 10x - 14y + 65 = 0$. Let $A$ be the product of all possible values of $a$ and $B$ be the product of all possible values of $b$. Then the value of $A + B$ is equal to.

$A$ variable line $ax + by + c = 0$,where $a, b, c$ are in $A.P.$,is normal to a circle $(x - \alpha)^2 + (y - \beta)^2 = \gamma$,which is orthogonal to the circle $x^2 + y^2 - 4x - 4y - 1 = 0$. The value of $\alpha + \beta + \gamma$ is equal to

If the circles $x^2+y^2=9$ and $x^2+y^2-8x-6y+n^2=0$,where $n \in \mathbb{Z}$,have exactly two common tangents,then the number of values for $n$ is

If the point $(2, \lambda)$ lies inside the circles $x^2+y^2=13$ and $x^2+y^2+x-2y=14$,then $\lambda$ lies in the set