Consider The Family Of Lines             (x + y – 1) + λ (2x + 3y – 5) = 0 And   (3x + 2y – 4) + µ (x + 2y – 6) = 0   Equation Of A Straight Line That Belongs To Both The Families Is:

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Consider the family of lines 

           (x + y – 1) + λ (2x + 3y – 5) = 0

and   (3x + 2y – 4) + µ (x + 2y – 6) = 0  

equation of a straight line that belongs to both the families is:


Correct option is

x – 2y + 8 = 0

The family of the lines 

                  (x + y – 1) + λ (2x + 3y – 5) = 0   

Passes through intersection of

           x + y – 1 = 0                               …(i)

         2x + 3y – 5 = 0                             … (ii)    

Solving (i) and (ii), we get (x1y1) ≡ (–2, 3)

Family of the line

             (3x + 2y – 4) + µ(x + 2y – 6) = 0  

Solving (iii) and (iv), we get:   

Equation of line belonging to both the families will pass through (x1y1) and (x2y2)


⇒      x – 2y + 8 = 0 belongs to both the families.



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