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

$A$ line $L$ intersects the lines $3x - 2y - 1 = 0$ and $x + 2y + 1 = 0$ at the points $A$ and $B$. If the point $(1, 2)$ bisects the line segment $AB$ and $\frac{x}{a} + \frac{y}{b} = 1$ is the equation of the line $L$,then $a + 2b + 1 = $

The equation of the lines on which the perpendiculars from the origin make a $30^\circ$ angle with the $x$-axis and which form a triangle of area $\frac{50}{\sqrt{3}}$ with the axes,are

Reduce the equation $\sqrt{3} x + y - 8 = 0$ into normal form. Find the values of $p$ and $\omega$.

If $a, b$ and $c$ are in $AP$, then the straight line $ax + 2by + c = 0$ will always pass through a fixed point whose coordinates are

In what ratio does the line $y - x + 2 = 0$ divide the line segment joining the points $(3, -1)$ and $(8, 9)$?