If $a x^2+6 x y-2 y^2=0$ represents a pair of perpendicular lines and $9 x^2+2 h x y+4 y^2=0(h>0)$ represents a pair of coincident lines, then $h=$

The line $x+2 y=k$ meets the curve $2 x^2-2 x y+3 y^2+2 x-y-1=0$ at two points $A$ and $B$. Let $O$ be the origin. If the line segments $O A$ and $O B$ are perpendicular to each other, then $k=$

Let the centre of the circle $S=0$ lie on the line $x+y-5=0$ and also lie in the first quadrant. If this circle touches both the lines $x-2=0$ and $y-5=0$, then the area of the circle is

The straight line $x+2 y=1$ cuts the $X$-axis at $A$ and $Y$-axis at $B, A$ circle is drawn through $A, B$ and the origin. The sum of the perpendicular distances from $A$ and $B$ on to the tangent drawn at origin to the circle $S$ is