The equation $r \cos \left(\theta-\frac{\pi}{3}\right)=2$ represents

Find the slope of the line passing through the points $(3, -2)$ and $(-1, 4)$.

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

If a line $L$ passes through the point of intersection of the lines $2x + 3y + 1 = 0$ and $x + y - 3 = 0$ and the angle made by the line $L$ with the $X$-axis measured in the positive direction from the positive $X$-axis is $\tan^{-1} \frac{2}{3}$,then the sum of the intercepts made by this line on the axes is

The equation of a line passing through the point $(1, 2)$ whose distance from the point $(3, 1)$ is the greatest is

The $x$-intercept and $y$-intercept of the line $2x - 3y = 6$ are respectively: