Question

If the sum of reciprocal of intercepts made by a line on the coordinate axes is $k$, then the line passes always through the point

• A. $(k,k)$
• B. $(\frac{1}{k},\frac{1}{k})$
• C. $(k,-k)$
• D. $(-k,k)$

Answer 1

The correct option is B $(\frac{1}{k},\frac{1}{k})$

Let the equation of the line be
$\frac{x}{a}+\frac{y}{b}=1$
Its intercept on $x-$axis and $y-$axis are $a$ and $b$ respectively.
Given, $\frac{1}{a}+\frac{1}{b}=k$
$\Rightarrow \frac{1}{ak}+\frac{1}{bk}=1$
$\Rightarrow \frac{1/k}{a}+\frac{1/k}{b}=1$
From here we can say that the line passes through the fixed point $(\frac{1}{k},\frac{1}{k})$