The distance of the point $(1, 2)$ from the line $x + y = 0$ measured parallel to the line $3x - y = 2$ is

$A$ straight line which makes equal intercepts on positive $X$ and $Y$ axes and which is at a distance $1$ unit from the origin intersects the straight line $y=2x+3+\sqrt{2}$ at $(x_0, y_0)$. Then $2x_0+y_0$ is equal to

The equation of a straight line passing through $(3, 2)$ and cutting an intercept of $2 \text{ units}$ between the lines $3x + 4y = 11$ and $3x + 4y = 1$ is:

If $a, b, c$ are in $A.P.$,then the straight line $ax + by + c = 0$ will always pass through the point

$A(-2, 3)$ is a point on the line $4x + 3y - 1 = 0$. If the points on the line that are $10$ units away from the point $A$ are $(x_1, y_1)$ and $(x_2, y_2)$,then $(x_1 + y_1)^2 + (x_2 + y_2)^2 =$

$A$ straight line passing through the origin $O$ meets the parallel lines $4x + 2y = 9$ and $2x + y + 6 = 0$ at the points $P$ and $Q$ respectively. Then the point $O$ divides the line segment $PQ$ in the ratio: