If the perpendicular drawn from the point $(2,-3)$ to the straight line $4 x-3 y+8=0$ meets it at $M(a, b)$ and $a^3-b^3=k^3$, then $k=$

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 $2 x^2+x y-6 y^2+k=0$ is the transformed equation of $2 x^2+x y-6 y^2-13 x+9 y+15=0$ when the origin is shifted to the point $(a, b)$ by translation of axes, then $k=$