If $(h, k)$ is the image of the point $(3, -4)$ with respect to the line $2x - 3y - 5 = 0$ and $(\ell, m)$ is the foot of the perpendicular from $(h, k)$ onto the line $3x + 2y + 12 = 0$,then $\ell h + mk + 1 =$ ?

If $2x + 3y = 5$ is the perpendicular bisector of the line segment joining the points $A\left(1, \frac{1}{3}\right)$ and $B$,then $B$ is equal to

Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5$,where $\lambda$ is a parameter. All these lines pass through a fixed point $P$. One of these lines (say $L$) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$,then the value of $d^2$ is

The image of a point $(2, -1)$ with respect to the line $x - y + 1 = 0$ is

The image of the point $P(3, 8)$ with respect to the line $x + 3y = 7$,assuming the line to be a plane mirror,is equal to .........

$A$ light ray along the line $x + \sqrt{3}y = \sqrt{3}$ reaches the $x$-axis and gets reflected. Find the equation of the reflected ray.