The length of the segment of the straight line passing through $(3,3)$ and $(7,6)$ cut off by the coordinate axes is

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 $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$,then $h^2+k^2=$

The points $A (1, 3)$ and $C (5, 1)$ are the opposite vertices of a rectangle. The equation of the line passing through the other two vertices and having a gradient of $2$ is:

The equation of the line bisecting the join of $(3, -4)$ and $(5, 2)$ and having its intercepts on the $x$-axis and the $y$-axis in the ratio $2 : 1$ is

The equation of the straight line making equal intercepts on the axes and passing through the point $(2, 4)$ is