$a$ and $b$ are the intercepts made by a line on the coordinate axes. If $3a = b$ and the line passes through $(1, 3)$,then the equation of the line is

The equation of the line passing through the point $(2,3)$ such that its $x$-intercept is twice its $y$-intercept is ......... .

The number of possible straight lines passing through the point $(2,3)$,while forming a triangle with coordinate axes enclosing an area of $12 \text{ sq. units}$ is

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

Find the angle in degrees $(^o)$ made by the line joining the points $(1, 0)$ and $(-2, \sqrt{3})$ with the $x$-axis.

$P(6,4)$ is a point on the line $x-y-2=0$. If $A(\alpha, \beta)$ and $B(\gamma, \delta)$ are two points on this line lying on either side of $P$ at a distance of $4$ units from $P$,then $\alpha^2+\beta^2+\gamma^2+\delta^2=$