The equation of the straight line which passes through the point $(1, -2)$ and cuts off equal intercepts from the axes is:

The equation of the straight line passing through $(-a, 0)$ and forming a triangle with the coordinate axes of area $T$ is

Find the value of $k$ for which the line $(k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0$ passes through the origin.

Find the equation of the line passing through the point $(3, 4)$ and making intercepts on the axes of equal magnitude but opposite signs.

The equation of the line passing through the origin and the point $(a \cos \theta, a \sin \theta)$ is .....

The straight line passing through the point of intersection of the straight lines $x - 3y + 1 = 0$ and $2x + 5y - 9 = 0$ and having infinite slope and at a distance of $2 \text{ units}$ from the origin,has the equation