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.

$P(6,4)$ 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 $\alpha^2+\beta^2+\gamma^2+\delta^2=$

$A$ straight line passing through the point $(2, 2)$ intersects the lines $\sqrt{3}x + y = 0$ and $\sqrt{3}x - y = 0$ at points $A$ and $B$ respectively. Find the equation of the line $AB$ such that the triangle $OAB$ is an equilateral triangle,where $O$ is the origin.

If $(a, -2a), a > 0$ is the midpoint of a line segment intercepted between the coordinate axes,then the equation of the line is

Find the coordinates of the point where the line $3x - 2y - 6 = 0$ intersects the $Y$-axis.

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