M L Aggarwal Solutions for Chapter: Straight Lines, Exercise 6: EXERCISE

Find the equation of a line which passes through $\left(2,2\right)$ and sum of its intercepts on the axes is $9$.

Find the equation of the line whose perpendicular distance from the origin is $5$ units and angle made by the perpendicular with the positive direction of $x-\mathrm{axis}$ is ${30}^0$.

If $p$ is the length of the perpendicular from origin to the line and $\alpha$ is the angle which this perpendicular makes with the positive direction of $x-\mathrm{axis}$, then sketch and write the equation of the line when: $p=3, \alpha ={45}^0$.

If $p$ is the length of the perpendicular from origin to the line and $\alpha$ is the angle which this perpendicular makes with the positive direction of $x-\mathrm{axis}$, then sketch and write the equation of the line when: $p=5, \alpha ={135}^0$.

If $p$ is the length of the perpendicular from origin to the line and $\alpha$ is the angle which this perpendicular makes with the positive direction of $x-\mathrm{axis}$, then sketch and write the equation of the line when: $p=1, \alpha ={90}^0$.

Find the equation of the line for which $p=2$ and $\sin \alpha =\frac{4}{5}$, where $p$ and $\alpha$ have usual meaning.

Find the equation of the line through $(-2,1)$ in symmetrical form when the angle made by the line with positive direction of $x-\mathrm{axis}$ is ${45}^0$.

A straight line passing through the point $A\left(2,3\right)$ has the inclination ${45}^0$ and intersects the line $2x-3y+9=0$ at point $P$. Find the distance $AP$.