Find the equation of a line perpendicular to the line $x-2y+3=0$ and passing through the point $(1, -2).$

Find the coordinates of the point where the line $3x - 2y - 6 = 0$ intersects the $Y$-axis.

Find the equation of the line passing through the point $(-2, 3)$ with a slope of $-4$.

The polar equation of the line perpendicular to the line $\sin \theta - \cos \theta = \frac{1}{r}$ and passing through the point $\left(2, \frac{\pi}{6}\right)$ is

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $OAB$ is $12$ sq. units. If the line passes through the point $(2,3)$,then the equation of the line is

The line passing through $(1, 0)$ and $(-2, \sqrt{3})$ makes an angle of ...... with the $x$-axis. (in $^o$)