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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. \[\] [ Hint : $\large\frac{x}{a}$$ + \large\frac{y}{b}$$=1$ where $ \large\frac{1}{a}$$+\large\frac{1}{b}$ = constant = $ \large\frac{1}{k}$ (say ). This implies that $ \large\frac{k}{a}$$+\large\frac{k}{b}$$=1 \Rightarrow $ line passes through the fixed point (k, k).]

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