﻿ 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: : Kaysons Education

# 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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## Question

### Solution

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.

#### SIMILAR QUESTIONS

Q1

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Q2

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Q9

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Q10

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