Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 4: INTRODUCTORY EXERCISE 2.4

$P$ is a point on either of the two lines $y-\sqrt{3}\left|x\right|=2$ at a distance of $5$ units from their point of intersection. The co-ordinates of the foot of the perpendicular from $P$ on the bisector of the angle between them are :

The equation of the straight line which bisects the intercepts made by the axes on the lines $x+y=2$ and $2x+3y=6$ is :

The equation of the bisector of the acute angle between the lines $2x-y+4=0$ and $x-2y=1$ is :

The equation of the bisector of that angle between the lines $x+y=3$ and $2x-y=2$ which contains the point $\left(1,1\right)$ is :

Equation of the base of an equilateral triangle is $3x+4y=9$ and its vertex is at the point $\left(1,2\right)$. Find the equations of the other sides and the length of each side of the triangle.

Find the co-ordinates of those points on the line $3x+2y=5$ which are equidistant from the lines $4x+3y-7=0$ and $2y-5=0$.

The bisector of two lines $L_1$ and $L_2$ are given by $3x^2-8xy-3y^2+10x+20y-25=0$. If the line $L_1$ passes through origin, find the equation of line $L_2$.

Find the equation of the bisector of the angle between the lines $x+2y-11=0$ and $3x-6y-5=0$ which contains the point $\left(1,-3\right)$.