NCERT Solutions for Chapter: Straight Lines, Exercise 1: EXERCISE

Find the equation of lines passing through $(1,2)$ and making angle $30°$ with $y$-axis.

For what values of $a$ and $b$ the intercepts cut off on the coordinate axes by the line $ax + by + 8 = 0$  are equal in length but opposite in signs to those cut off by the line $2x - 3y + 6 = 0$ on the axes.

If the intercept of a line between the coordinate axes is divided by the point $(-5,4)$ in the ratio $1:2,$ then find the equation of the line.

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of $120°$ with the positive direction of $x$-axis.[Hint: Use normal form, here $\omega =30°$].

Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by $3x+4y=4$ and the opposite vertex of the hypotenuse is $(2,2)$.

Find the equation of the line which passes through the point $(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5:3$ by this point.

Find the equations of the lines through the point of intersection of the lines $x-y+1=0$ and $2x-3y+5=0$ and whose distance from the point $\left(3,2\right)$ is $\frac{7}{5}$. 

If the sum of the distances of a moving point in a plane from the axes is $1$, then find the locus of the point.

[Hint: Given that $\left|x\right|+\left|y\right|=1,$ which gives four sides of a square.]