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  4. If the line (x-y+1) + k (y-2x+4) = 0 makes equal intercept on the axes then the value of k is

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Q. If the line (x-y+1) + k (y-2x+4) = 0 makes equal intercept on the axes then the value of k is

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Solution:

Given line is $ (x-y+1)+k (y-2x+4)=0$
$\Rightarrow x-y+1+k y- 2kx+4k = 0$
$\Rightarrow (1-2 k) x+(k-1) y+(1+4 k)=0$ ...(1)
Since line (1) makes Equal intercepts on the coordinate axes.
i.e. $x$ -intercent $=y$ -intercept
$\Rightarrow \frac{-(1+4 k)}{1-2 k}=\frac{-(1+4 k)}{k-1}$
$\Rightarrow \frac{1}{1-2 k} =\frac{1}{k-1}$
$\Rightarrow k-1 =1-2 k$
$\Rightarrow k+2 k =1+1$
$\Rightarrow 3 k =2$
$\Rightarrow k =\frac{2}{3}$