Question:
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
Solution:
We know that intercepts form of a straight line is
$\frac{x}{a}+\frac{y}{b}=1$
Where $a$ and $b$ are the intercepts on the axes
Given that $\frac{1}{a}+\frac{1}{b_{k}}=\frac{1}{k}$ (let)
On cross multiplication we get
$\Rightarrow \frac{k}{a}+\frac{k}{b}=1$
This shows that the line is passing through the fixed point ( $k, k$ )
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