Question

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

• A. $\frac{1}{3}$
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (D)

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