Find the equation of the line passing through $(4, 6)$ and parallel to the line $3x - 7y + 2 = 0$.

The line passing through $(-1, \pi/2)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is

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

Find the equation of the line which intersects the $x$-axis at a distance of $3$ units to the left of the origin with a slope of $-2$.

$A$ line through the point $A(2,0)$ which makes an angle of $30^{\circ}$ with the positive direction of $x$-axis is rotated about $A$ in clockwise direction through an angle $15^{\circ}$. Then the equation of the straight line in the new position is

The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90^\circ + \alpha)$ with the positive direction of the $X$-axis is: