If the points $(-2, -5)$,$(2, -2)$,and $(8, a)$ are collinear,then the value of $a$ is (in $.5$)

Reduce the equation $y-2=0$ into the normal form $x \cos \omega + y \sin \omega = p$. Find the perpendicular distance from the origin $(p)$ and the angle between the perpendicular and the positive $x$-axis $(\omega)$.

$A$ man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$. Three stones $A, B$ and $C$ are placed at the points $(1,1), (2,2)$ and $(4,4)$ respectively. Which of these stones is/are on the path of the man?

Let $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$,then $h^2+k^2=$

Find the equation of the line passing through the point $(2, 3)$ and perpendicular to the line joining the points $(-5, 6)$ and $(-6, 5)$.

If a line $L$ passing through the point $A(-2, 4)$ makes an angle of $60^{\circ}$ with the positive direction of $X$-axis in the anti-clockwise direction and $B(p, q)$ lying in the $3^{\text{rd}}$ quadrant is a point on $L$ at a distance of $6$ units from the point $A$,then $\sqrt{p^2+q^2-8q} = $