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A straight line cuts intercepts from the axes of coordinates the sum of the reciprocals of which is a constant. Show that it always passes through a fixed point.

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Its intercepts on the x and y axes are a and b respectively.

It is given that

1/a + 1/b = constant = k (assume)

1/ka + 1/kb = 1

According to the given condition :

Hence 1/k, 1/k satisfies equation.

x/a + y/b = 1

Hence the line passes through the fixed point (1/k, 1/k)

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