Question

 

Find the equations of the bisectors of the angle between the coordinate axes.

 

Solution

Correct option is

x ± y = 0

 

Let L1 and L2 be the straight lines bisecting the coordinate axes,   

Both L1 and L2 pass through origin  

∴ Equation of line through origin is y = mx for L1m = tan 45o = 1

∴ Equation of line L1 is       y = x                

i.e.         x – y = 0

For L2m = tan 135o = –1 

∴ Equation of line L2 is      y = –x

i.e.        x + y = 0     

Hence equations of the bisectors of the angle between the coordinate axes are x ± y = 0.

SIMILAR QUESTIONS

Q1

 

A line passes through the points A(2, –3) and B(6, 3). Find the slopes of the lines which are  

1. parallel to AB

2. perpendicular to AB

Q2

 

Find the equation of the straight line parallel to y-axis and at a distance  

(i).3 units to the right

(ii). 2 units to the left

Q3

 

Find the equation of the straight line parallel to x-axis and at a distance

(i). 5 units above the x-axis

(ii). 9 units below the x-axis

Q4

 

Find the equation of the straight line which passes through the point (2, –3) and is  

1. parallel to the x-axis

2. perpendicular to the x-axis

Q5

Find the equation of a line which is equidistant from the lines .

Q6

If the straight line y = mx + c passes through the points (2, 4) and (–3, 6), find the values of m and c.

Q7

 

What are the inclination to the x-axis and intercept on y-axis of the line 

              ?

Q8

Find the equation of the straight line cutting off an intercept of 3 units on negative direction of y-axis and inclined at an angle  to the axis of x.

Q9

Find the equation to the straight line cutting off an intercept of 5 units on negative direction of y-axis and being equally inclined to the axes.  

Q10

Find the equation of a line which makes an angle of 135o with positive direction of x-axis and passes through the point (3, 5).