Home
Class 11
MATHS
The equation of the pair of lines throug...

The equation of the pair of lines through the point (a,b) parallel to the coordinates axes, is

A

`(x-a)(y+b)=0`

B

`(a-b)(y-a)=0`

C

`(x-a)(y-b)=0`

D

`(x+a)(y-b)=0`

Text Solution

AI Generated Solution

The correct Answer is:
To find the equation of the pair of lines through the point (a, b) that are parallel to the coordinate axes, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Point**: We have the point (a, b) through which the lines will pass. 2. **Understand Parallel Lines**: Since the lines are parallel to the coordinate axes, we will have one line parallel to the x-axis and another line parallel to the y-axis. 3. **Equation of the Line Parallel to the x-axis**: The line parallel to the x-axis that passes through (a, b) will have a constant y-value. Therefore, the equation of this line is: \[ y = b \] This can also be written in the standard form as: \[ y - b = 0 \] 4. **Equation of the Line Parallel to the y-axis**: The line parallel to the y-axis that passes through (a, b) will have a constant x-value. Therefore, the equation of this line is: \[ x = a \] This can also be written in the standard form as: \[ x - a = 0 \] 5. **Combined Equation of the Pair of Lines**: The combined equation of the two lines can be expressed as: \[ (x - a)(y - b) = 0 \] This indicates that either \(x - a = 0\) or \(y - b = 0\), which corresponds to the two lines we derived. ### Final Answer: The equation of the pair of lines through the point (a, b) parallel to the coordinate axes is: \[ (x - a)(y - b) = 0 \]
To find the equation of the pair of lines through the point (a, b) that are parallel to the coordinate axes, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Point**: We have the point (a, b) through which the lines will pass. 2. **Understand Parallel Lines**: Since the lines are parallel to the coordinate axes, we will have one line parallel to the x-axis and another line parallel to the y-axis. ...
Promotional Banner

Similar Questions

Explore conceptually related problems

The joint equation of pair of lines through point (a, b) parallel to the co-ordinate axes is

Write an equation representing a pair of lines through the point (a , b) and parallel to the coordinate axes.

The joint equation of the pair of lines passing through (2, 3) and parallel to the coordinate axes is

a pair of lines passing through the point (3,d) and parallel to coordinate axes

Find the combined equation of the pair of lines through the point (1,0) and parallel to the lines represented by 2x^(2)-xy-y^(2)=0

Find the equation of the straight line through the point P(a,b) parallel to the line x/a+y/b = 1 also find the intercepts made by it on the axes .

The equation to the pair of lines passing through the point (-2,3) and parallel to the pair of lines x^(2)+4xy+y^(2)=0 is

The equation of the straigh lines through the point (x_(1),y_(1)) and parallel to the lines given by ax^(2)+2xy+ay^(2)=0 , is

The combined equation of the pair of the straight lines through the point (1, 0) and parallel to thelines represented by 2x^(2)-xy-y^(2)=0 is

Combined equation of pair of lines, through (1,2) and parallel to co-ordinate axes is