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

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

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

For what values of $a$ and $b$ are the intercepts cut off on the coordinate axes by the line $ax + by + 8 = 0$ equal in length but opposite in sign to those cut off by the line $2x - 3y + 6 = 0$ on the axes?

If each of the points $(a, 4)$ and $(-2, b)$ lies on the line joining the points $(2, -1)$ and $(5, -3)$,then the point $(a, b)$ lies on the line:

If $\alpha$ is the angle made by the perpendicular drawn from the origin to the line $12x - 5y + 13 = 0$ with the positive $X$-axis in the anti-clockwise direction,then $\alpha =$