R D Sharma Solutions for Chapter: The Straight Lines, Exercise 7: EXERCISE 23.7

Find the equation of a line whose perpendicular distance from the origin is $8$ units, and the angle which the normal makes with positive direction of $x$-axis is $225°$.

Find the equation of a line whose perpendicular distance from the origin is $8$ units, and the angle which the normal makes with positive direction of $x$-axis is $300°$.

Find the equation of the line on which the length of the perpendicular segment from the origin to the line is $4$ units and the inclination of the perpendicular segment with the positive direction of $x-$axis is $30°.$

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 $x-$axis is $15°$

Find the equation of the straight line at a distance of $3$ units from the origin such that the perpendicular from the origin to the line makes an angle ${\tan }^{-1}$ $\left(\frac{5}{12}\right)$ with the positive direction of $x-$axis.

The length of the perpendicular from the origin to a line is $7$ and the line makes an angle of $150°$ with the positive direction of $Y-$axis. Find the equation of the line.

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

Find the equation of the straight line which makes a triangle of area  $96\sqrt{3}$ with the axes and perpendicular from the origin to it makes an angle of $30°$ with $y-$axis.