Find the equation of the line perpendicular to the line $ax + by + c = 0$ and passing through the point $(a, b)$.

$A$ ray of light along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching the $x$-axis. The equation of the reflected ray is:

Let $A \left(\frac{3}{\sqrt{a}}, \sqrt{a}\right)$ with $a > 0$ be a fixed point in the $xy$-plane. The image of $A$ in the $y$-axis is $B$,and the image of $B$ in the $x$-axis is $C$. If $D(3 \cos \theta, a \sin \theta)$ is a point in the fourth quadrant such that the maximum area of $\triangle ACD$ is $12$ square units,then $a$ is equal to:

If the image of point $P(2, 3)$ in a line $L$ is $Q(4, 5)$,then the image of point $R(0, 0)$ in the same line is

If the reflection of a point $A(2,3)$ in the $X$-axis is $B$; the reflection of $B$ in the line $x+y=0$ is $C$,and the reflection of $C$ in $x-y=0$ is $D$,then the point of intersection of the lines $CD$ and $AB$ is:

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