Question

Consider the family of lines (x + y – 1) + l (2x + 3y – 5) = 0 & (3x + 2y – 4) + m (x + 2y – 6) = 0, then the equation of a straight line that belongs to both the families is:

• A. x – 2y – 8 = 0
• B. x – 2y + 8 = 0
• C. 2x + y – 8 = 0
• D. 2x – y – 8 = 0

Answer 1

Answer: (B)

x – 2y + 8 = 0

Answer 2

If lines (i) and (ii) are same then

$\frac { 2 \lambda + 1 } { \mu + 3 } = \frac { 3 \lambda + 1 } { 2 \mu + 2 } = \frac { 5 \lambda + 1 } { 6 \mu + 4 }$

Solve it value of l = $- \frac { 3 } { 7 }$

Required line x – 2y + 8 = 0