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

The locus of the centre of the circle which touches the circle ${x^2} + {(y - 1)^2} = 1$ externally and also touches the $x$-axis is

$A$ circle with centre $P$ is tangent to the negative $x$-axis and negative $y$-axis and is externally tangent to a circle with centre $(-6, 0)$ and radius $2$. What is the sum of all possible radii of the circle with centre $P$?

If $(x, y)$ is a variable point on the curve $x^2 + y^2 - 2x - 2y - 2 = 0$,then the minimum value of the expression $\frac{8}{(x - 1)^2} - \frac{(y - 1)^2}{4}$ is equal to

Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16x$. If one of these tangents touches the two curves at $Q$ and $R$,then $(QR)^2$ 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