If the perpendicular drawn from the point $(2, -3)$ to the straight line $4x - 3y + 8 = 0$ meets it at $M(a, b)$ and $a^3 - b^3 = k^3$,then $k=$

If the coordinates of the points $A, B, C$ are $(-1, 5), (0, 0)$ and $(2, 2)$ respectively and $D$ is the midpoint of $BC$,then the equation of the perpendicular drawn from $B$ to the line $AD$ is

If $(\alpha, \beta)$ is the image of the point $(3, -4)$ with respect to the line $4x - y - 1 = 0$,then the value of $\beta - \alpha$ is equal to

$N(3, -4)$ 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 along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching the $x$-axis. The equation of the reflected ray is:

The polar coordinates of $P$ are $\left(2, \frac{\pi}{6}\right)$. If $Q$ is the image of $P$ about the $X$-axis,then the polar coordinates of $Q$ are...