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 axis, its equation is  

  • Option 1)

    25x+25y-1=0

  • Option 2)

    5x-5y+3=0

  • Option 3)

    25x+25y-4=0

  • Option 4)

    25x-25y+6=0

 

Answers (1)

 

Family of straight lines -

L_{1}+\lambda L_{2}=0


 

- wherein

 L_{1}\, and \, L_{2}=0 are the equations of the lines and \lambda is a constant.

 

 family of lines:

(100x+50y-1)+\lambda (75x+25y+3) = 0

\Rightarrow (100+75\lambda )x + (50+25\lambda )y = 1-3\lambda

\Rightarrow \lambda -intercept = \frac{1-3\lambda }{100+75\lambda } & \gamma - intercept = \frac{1-3\lambda }{50+25\lambda }

So, equal intercepts mean

100+75\lambda = 50+25\lambda

\Rightarrow 50 = -50\lambda \Rightarrow \lambda = - 1
25x+25y=4
\Rightarrow 25x+25y-4=0


Option 1)

25x+25y-1=0

This solution is incorrect.

Option 2)

5x-5y+3=0

This solution is incorrect.

Option 3)

25x+25y-4=0

This solution is incorrect.

Option 4)

25x-25y+6=0

This solution is incorrect.

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