The equation of the line passing through the points $(1, 2)$ and $(2, 5)$ is:

Find the equation of the line whose perpendicular distance from the origin is $4$ units and the angle which the normal makes with the positive direction of the $x$-axis is $15^{\circ}$.

The equation of the line which makes a right-angled triangle with the axes whose area is $6$ sq. units and whose hypotenuse is $5$ units,is

Find the values of $\theta$ and $p$,if the equation $x \cos \theta + y \sin \theta = p$ is the normal form of the line $\sqrt{3} x + y + 2 = 0$.

The equation of the line passing through $(1, 2)$ and parallel to the line $y = 3x - 1$ is

The equation of the line making an angle of $135^\circ$ with the positive $x$-axis and having a $y$-intercept equal to $-2$ is: