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 coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The coordinates of the point $A$ are:

The value of $a$ for which the image of the point $(a, a - 1)$ with respect to the line mirror $3x + y = 6a$ is the point $(a^2 + 1, a)$ is:

If $B$ is the reflection of the point $A(1, 2)$ with respect to the line $y = x$ and $(\alpha, \beta)$ is the reflection of $B$ with respect to $y = 0$,then-

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 $\ell h + mk + 1 =$ ?

$A$ ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0, 1)$ and is then reflected from this point along the line $y + 2x = 1$. Then the equation of the line of incidence of the ray of light is