If the line passing through the points $(4, 3)$ and $(2, \lambda)$ is perpendicular to the line $y = 2x + 3$,then find the value of $\lambda$.

The equation of a line,whose perpendicular distance from the origin is $7$ units and the angle,which the perpendicular to the line from the origin makes,is $120^{\circ}$ with the positive $X$-axis,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

$P(6,4)$ is a point on the line $x-y-2=0$. If $A(\alpha, \beta)$ and $B(\gamma, \delta)$ are two points on this line lying on either side of $P$ at a distance of $4$ units from $P$,then $\alpha^2+\beta^2+\gamma^2+\delta^2=$

The intercept cut off from the $y$-axis is twice that from the $x$-axis by a line,and the line passes through $(1, 2)$. Find its equation.

Reduce the following equation into intercept form and find its intercepts on the axes: $3x + 2y - 12 = 0$.