Question

If the sum of reciprocals of intercepts made by a straight line on the co-ordinate axes is a constant $K$, then the line will always pass through the point

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

Answer 1

The correct option is C $(\frac{1}{K},\frac{1}{K})$

Let the equation of line be
$\frac{x}{a}+\frac{y}{b}=\mathrm{1...}\left(i\right)$
Where $a,b$ are the intercepts.So according to question :
$\frac{1}{a}+\frac{1}{b}=K$
$\Rightarrow \frac{1}{Ka}+\frac{1}{Kb}=1$

$\Rightarrow \frac{\frac{1}{K}}{a}+\frac{\frac{1}{K}}{b}=\mathrm{1...}\left(ii\right)$

Comparing equation $\left(i\right)$ and $\left(ii\right)$ the line will always pass through $(\frac{1}{K},\frac{1}{K})$