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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.

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.

Answers (1)

Equation of line in intercept form=xa+yb=1

 where a and b are intercepts on the axes 

Given that \frac{1}{a}+\frac{1}{b}=\frac{1}{k}

  Then, \frac{k}{a}+\frac{k}{b}=1

This shows that the line is passing through the fixed point that is (k,k)

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infoexpert22

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