The point $P(4,1)$ undergoes the following transformations in succession :

(i) origin is shifted to the point $(1,6)$ by translation of axes.

(ii) translation through a distance of 2 units along the positive direction of $X$-axis.

(iii) rotation of axes through an angle of $90^{\circ}$ in the positive direction.

Then, the coordinates of the point $P$ in its final position are

$L_1 \equiv a x-3 y+5=0$ and $L_2 \equiv 4 x-6 y+8=0$ are two parallel lines. If $p, q$ are the intercepts made by $L_1=0$ and $m, n$ are the intercepts made by $L_2=0$ on the $X$, $Y$-coordinate axes respectively, then the equation of the line passing through the points $(p, q)$ and $(m, n)$ is

If $(h, k)$ is the image of the point $(2,-3)$ with respect to the line $5 x-3 y=2$, then $h+k=$

If the pair of lines $a x^2-7 x y-3 y^2=0$ and $2 x^2+x y-6 y^2=0$ have exactly one line in common and ' $a$ ' is an integer, then the equation of the pair of bisectors of the angles between the lines $a x^2-7 x y-3 y^2=0$ is