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# Try this! 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

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)
329 Views

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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