$a$ and $b$ are the intercepts made by a line on the coordinate axes. If $3a = b$ and the line passes through $(1, 3)$,then the equation of the line is

$A$ straight line passes through the point $A(3, 4)$ such that its intercept between the axes is bisected at $A$. Find its equation.

If the straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive direction of $X$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$,then the length of $PQ$ is

The area of a triangle formed by a line with the coordinate axes is $49 \text{ sq. units}$. If the perpendicular drawn from the origin to this line makes an angle of $45^\circ$ with the positive $X$-axis, then the equation of the line is:

If we reduce $3x + 3y + 7 = 0$ to the form $x \cos \alpha + y \sin \alpha = p$,then the value of $p$ is

Consider the equation $y-y_1=m(x-x_1)$. If $m$ and $x_1$ are fixed and different lines are drawn for different values of $y_1$, then