Let the line $2 x-3 y-1=0$ intersect the curve $x^2+2 x y+5 y^2+2 x+3 y-1=0$ in distinct points $A$ and $B$. If ' $O$ ' is the origin, then $\cos \angle A O B=$

If $\alpha$ is the angle made by the perpendicular drawn from origin to the line $3 x-4 y+5=0$ with positive $X$-axis in positive direction and $a x+b y=1$ is the equation of a line passing through the point $(1,-1)$ with $\tan \alpha$ as its slope, then $a+a b+b=$

If $L_1$ is a line passing through the point $P(4,-3)$ and perpendicular to the line $3 x-4 y+k=0$ then the distance of $P$ from the line $5 x-3 y-2=0$ measured along the line $L_1$ is

Let the line $L_1$ passing through the point of intersection of the lines $2 x+3 y-5=0$ and $4 x-5 y+7=0$ divide the line segment joining the points $(2,3)$ and $(1,-1)$ in the ratio $2: 1$. If the equation of $L_1$ is $a x+b y=1$, then $33(a-b)=$