The equation of the line,which bisects the line segment joining the points $(2, -19)$ and $(6, 1)$ and is perpendicular to the line joining the points $(-1, 3)$ and $(5, -1)$,is

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

If $a, b$ are positive real numbers such that the lines $ax + 9y = 5$ and $4x + by = 3$ are parallel,then the least possible value of $a + b$ is

$A$ line cuts the $X$ and $Y$ axes at the points $A$ and $B$ respectively. If the point $(5, 6)$ divides the line segment $AB$ internally in the ratio $3: 1$,then the equation of the line is:

The line passing through $\left(-1, \frac{\pi}{2}\right)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is:

$A$ straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^o$ with the line $x + y = 0$. Then an equation of the line $L$ is