Question

 

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.

Solution

Correct option is

23x + 23y = 11

 

Equation of any line passing through the intersection of the given lines is  

      (3x – 4y + 1) + λ(5x + y – 1) = 0   

  

  

but given     x-intercept = y-intercept  

  

   (λ ≠ 1 âˆµ if λ = 1 then line (i) pass through origin)

  

  

  

Substituting the value of λ in (i), we get required equation is

23x + 23y = 11.

SIMILAR QUESTIONS

Q1

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.

Q2

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.

Q3

 

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

 5x – 12y – 3 = 0.

Q4

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

Q5

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

Q6

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.

Q7

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

Q8

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.

Q9

 

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

Q10

Find the orthocentre of the triangle of the triangle ABC whose angular points are A(1, 2), B(2, 3) and C(4, 3).