$O(0,0)$ and $A(1,0)$ are centres of two units circles $C_1$ and $C_2$, respectively. $C_3$ is also a unit circle having its centre above $X$ - axis and passing through $O$ and $A$. The equation of the common tangent to $C_1$ and $C_3$ which does not intersect the circle $C_2$ is

If the circles $x^2+y^2-16 x-20 y+164=r^2(r>0)$ and $x^2+y^2-8 x-14 y+29=0$ intersect in two distinct points, then the maximum possible integral value of $r$ is

If the circle $x^2+y^2-6 x-12 y+1=0$ cuts another circle $C$ orthogonally and the centre of the circle $C$ is $(-4,2)$, then its radius of

Let $L L^{\prime}$ be the latusrectum and $P Q$ be the focal chord of the parabola $y^2=16 x$. If $P=(1,4)$ and $P, L$ lie in the same quadrant, then $L Q=$