If the coordinates of the points $A, B, C, D$ are $(a, b), (a', b'), (-a, b)$ and $(a', -b')$ respectively,then the equation of the line bisecting the line segments $AB$ and $CD$ is

The equation of the line passing through $(4, -6)$ and making an angle of $45^\circ$ with the positive $x$-axis is:

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is

Find the value of $k$ for which the line $(k-3)x - (4-k^2)y + k^2 - 7k + 6 = 0$ is parallel to the $x$-axis.

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 equations of the lines which pass through the point of intersection of the lines $4x - 3y - 1 = 0$ and $2x - 5y + 3 = 0$ and are equally inclined to the axes are