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 $PM$ is the perpendicular from $P(2, 3)$ onto the line $x + y = 3$,then the coordinates of $M$ are

Sum of values of $k$ for which the image of the point $(\lambda^2 + 1, \lambda)$ with respect to the line $y = -3x + 6k$ is the point $(\lambda, \lambda - 1)$ is:

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

Let $0 < \alpha < \pi/2$ be a constant angle. If $P \equiv (\cos \theta, \sin \theta)$ and $Q \equiv (\cos(\alpha - \theta), \sin(\alpha - \theta))$,how is $Q$ obtained from $P$?

Suppose $A$ and $B$ are two points on the line $2x - y + 3 = 0$ and $P(1, 2)$ is a point such that $PA = PB$. Then,the mid-point of $AB$ is