If the equation of the pair of straight lines passing through the point $(1,1)$ and perpendicular to the pair of lines $3 x^2+11 x y-4 y^2=0$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+12=0$, then $2(a-h+b-g+f-12)=$

If a variable straight line passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y-1=0$ intersects the $X, Y$-axes at $A$ and $B$ respectively, then the equation of the locus of a point which divides the segment $A B$ in the ratio $-2: 3$ is

Point $(-1,2)$ is changed to $(a, b)$, when the origin is shifted to the point $(2,-1)$ by translation of axes, Point $(a, b)$ is changed to $(c, d)$, when the axes are rotated through an angle of $45^{\circ}$ about the new origin, $(c, d)$ is changed to $(e, f)$, when $(c, d)$ is reflected through $y=x$. Then, $(e, f)=$

The point $(a, b)$ is the foot of the perpendicular drawn from the point $(3,1)$ to the line $x+3 y+4=0$. If $(p, q)$ is the image of $(a, b)$ with respect to the line $3 x-4 y+11=0$, then $\frac{p}{a}+\frac{q}{b}=$