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

The correct option is D $\frac{2}{3}$

$\frac{x}{a}+\frac{y}{b}=1$
$\text{Given equal intercept}\text{So,}a=b$ $\text{taken}x+y=a\Rightarrow \text{Slope is}-1$
Now $x(1-2k)+y(k-1)+1+4k=0$
$\text{Slope}=\frac{(1-2k)}{-(k-1)}=-1$
$\frac{(1-2k)}{-(k-1)}=-1$
$1-2k=k-1$
$3k=2$
$k=\frac{2}{3}$