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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.
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Solution
Intercepts form of a straight line is `x/a + y/b` = 1
Where a and b are the intercepts made by the line on the axes.
Given that: `1/a + 1/b = 1/k` (say)
⇒ `k/a + k/b` = 1
Which shows that the line is passing through the fixed point (k, k).
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