Let $Q$ be the image of a point $P(1,2)$ with respect to the line $x+y+1=0$ and $R$ be the image of $Q$ with respect to the line $x-y-1=0$. If $M$ and $N$ are the mid-points of $P Q$ and $Q R$ respectively, then $M N=$

If the slopes of the lines represented by the equation $6 x^2+2 h x y+4 y^2=0$ are in the ratio $2: 3$, then the value of $h$ such that both the lines make acute angles with the positive $X$-axis measured in positive direction is

If $(3,-2)$ is the centre of the circle $S \equiv x^2+y^2+2 g x+2 f y-23=0$ and $A$ is a point on the circle $S=0$ such that its distance from a point $P(-1,-5)$ is least, then $A=$

Two circles which touch both the coordinate axes intersect at the points $A$ and $B$. If $A=(1,2)$, then $A B=$