Question

Set of lines $(x-2y+1)+\lambda (x+y)=0$ (where $\lambda$ is a parameter) passing through a fixed point :

• A. $(\frac{1}{3},-\frac{1}{3})$
• B. $(-\frac{1}{3},\frac{1}{3})$
• C. $(1,1)$
• D. $noneofthese$

Answer 1

The correct option is B $(-\frac{1}{3},\frac{1}{3})$

Equation of set of lines is (x-2y+1) +$\lambda$(x+y)=0

where( $\lambda$ is the parameter)

This lines set of lines contains these two lines x-2y+1=0--(I)and x+y=0--(II)

So, By solving equation I and II, we get the required point:

$x=-\frac{1}{3}$

$y=\frac{1}{3}$

Hence, Option B is correct.