Find the equation of a straight line passing through $(-5, 6)$ and cutting off equal intercepts on the coordinate axes.

Let the coordinates of the two points $A$ and $B$ be $(1, 2)$ and $(7, 5)$ respectively. The line $AB$ is rotated through $45^{\circ}$ in the anti-clockwise direction about the point of trisection of $AB$ which is nearer to $B$. The equation of the line in the new position 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 $h^2+k^2=$

What are the coordinates of a point on the line $2x + 3y + 7 = 0$ which is at a distance of $3$ units from the point $(1, -3)$?

The equation of a line passing through the origin and perpendicular to the line joining $(a, 0)$ and $(-a, 0)$ is

If $PS$ is the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$ and $R(7,3)$,then the equation of the line passing through $(1,-1)$ and parallel to $PS$ is