Question

A line passes through the point of intersection of the lines $100x+50y-1=0$ and $75x+25y+$ $3=0$ and makes equal intercepts on the axes. Its equation is

• A. $25x+25y-1=0$
• B. $5x-5y+3=0$
• C. $25x+25y-4=0$
• D. $25x-25y+6=0$
• E. $5x-5y+7=0$

Answer 1

Answer: (C)

Equation of intersection of lines is
$(100x+50y-1)+\lambda (75x+25y+3)=0$
$\Rightarrow$ $(100+75\lambda )x+(50+25\lambda )y=1-3\lambda$ ?..(i)
$\Rightarrow$ $\frac{x}{\frac{1-3\lambda }{100+75\lambda }}+\frac{y}{\frac{1-3\lambda }{50+25\lambda }}=1$
According to the given condition
$\frac{1-3\lambda }{100+75\lambda }=\frac{1-3\lambda }{50+25\lambda }$
$\Rightarrow$ $50=-50\lambda \Rightarrow \lambda =-1$
$\therefore$ From Eq. (i), $25x+25y-4=0$