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Consider the family of lines 5 x+3 y-2+\lambda_1(3 x-y-4)=0  and x-y+1+\lambda_2(2 x-y-2)=0 Equation of a straight line that belong to both families is -

Option: 1

25 x-62 y+86=0


Option: 2

62 x-25 y+86=0


Option: 3

25 x-62 y=86


Option: 4

5 x-2 y-7=0


Answers (1)

Lines 5 x+3 y-2+\lambda_1(3 x-y-4)=0  are concurrent at (1, – 1) and lines 
\mathrm{x}-\mathrm{y}+1+\lambda_2(2 \mathrm{x}-\mathrm{y}-2)=0  are concurrent at (3, 4). Thus equation of line common to both family is, 
y-4=\frac{-1-4}{1-3}(x-3)
\text { i.e., } \quad 5 x-2 y-7=0 \text {. }

Posted by

Sumit Saini

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