Find The Equation Of The Line Passing Through The Point Of Intersection Of The Lines           x + 5y + 7 = 0, 3x + 2y – 5 = 0 And    1. Parallel To The Line 7x + 2y – 5 = 0 2. Perpendicular To The Line 7x + 2y – 5 = 0

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Question

 

Find the equation of the line passing through the point of intersection of the lines

          x + 5y + 7 = 0, 3x + 2y – 5 = 0 and   

1. parallel to the line 7x + 2y – 5 = 0

2. perpendicular to the line 7x + 2y – 5 = 0

Solution

Correct option is

2x – 7y – 20 = 0

 

Any line passing through the point of intersection of the given lines is   

      

  

       

1. Line (i) is to be parallel to 7x + 2y – 5 = 0

   

  

  

  

Substituting this value of λ in equation (i), we get the required equation as 7x + 2y – 17 = 0 

 

2. Line (i) is to be perpendicular to 7x + 2y – 5 = 0   

  

  

Substituting this value of λ is eq. (i), we get the required equation as  

       2x – 7y – 20 = 0   

 

Alternative Method : The point of intersection of the given lines

       x + 5y – 7 = 0 and 3x + 2y – 5 = 0 is (3, –2)   

∴ Equation of line through (3, –2) is 

       y + 2 = m(x – 3)                                    … (ii)   

1. Line (ii) is parallel to 7x + 2y – 5 = 0 

  

Hence the equation of the required line is  

       

or    7x + 2y – 17 = 0 

 

2. Line (ii) is perpendicular to 7x + 2y – 5 = 0   

  

   

Hence the equation of the required line is   

 

 

or     2x – 7y – 20 = 0

Testing

SIMILAR QUESTIONS

Q1

Find the general equation of the line which perpendicular to x + y + 4 = 0. Also find such line through the point (1, 2).   

Q2

Find the sum of the abscissas of all the points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y – 10 = 0.

Q3

If p and p’ are the length of the perpendiculars from the origin to the straight line whose equations are , then find the value of 4p2 + p2.

Q4

 

Find the distance between the lines 5x – 12y + 2 = 0 and

 5x – 12y – 3 = 0.

Q5

Find the equations of the line parallel to 5x – 12y + 26 = 0 and at a distance of 4 units from it.

Q6

If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 (ab and cbeing distinct and difference from 1) are concurrent, then find the value of

Q7

Find the equation of the straight line passing through the point (2, 1) and through the point of intersecction of the lines x + 2y = 3 and 2x – 3y = 4.

Q8

The family of lines x(a + 2b) + y(+ 3b) = b passes through the point for all values of a and b. Find the point.

Q9

If 3a + 2b + 6c = 0 the family of straight lines ax + by + c = 0 passes through a fixed point. Find the coordinates of fixed point.

Q10

 

Find the equation of straight line which passes through the intersection of the straight lines  

        3x – 4y + 1 = 0 and 5x + y – 1 = 0 

and cuts off equal intercepts from the axes.