$N(3, -4)$ is the foot of the perpendicular drawn from the origin to a line $L$. Then the equation of the line $L$ is

$A$ 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:

If the perpendicular bisector of the line segment joining the points $P(1, 4)$ and $Q(k, 3)$ has a $y$-intercept equal to $-4$,then a value of $k$ is

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

If $(-2, 6)$ is the image of the point $(4, 2)$ with respect to the line $L = 0$,then $L$ is equal to

The distance between the point $(2, 1)$ and the image of the point $(3, -1)$ with respect to the line $2x + y - 1 = 0$ is