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

$A$ line $L$ intersects the lines $3x - 2y - 1 = 0$ and $x + 2y + 1 = 0$ at the points $A$ and $B$. If the point $(1, 2)$ bisects the line segment $AB$ and $\frac{x}{a} + \frac{y}{b} = 1$ is the equation of the line $L$,then $a + 2b + 1 = $

The equation of a given straight line is $\frac{x-x_1}{\cos \theta}=\frac{y-y_1}{\sin \theta}=\gamma$. If the equation of the line perpendicular to the given line and passing through $(\alpha, \beta)$ is $\frac{x}{a}+\frac{y}{b}=1$,then $\frac{b}{a}$ is equal to

$A$ line passes through $P(-4, 1)$ and meets the coordinate axes at points $A$ and $B$. If $P$ divides the segment $AB$ internally in the ratio $1:2$,then the equation of the line is

Reduce the following equation into intercept form and find its intercepts on the axes: $4x - 3y = 6$.

$\beta$ is the angle made by the perpendicular drawn from the origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If '$a$' is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance from the origin to the line $L=0$,then $a \tan \beta + p^2 =$