Question

A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through.

• A. A fixed point
• B. A variable point
• C. Origin
• D. None of these

Answer 1

Answer: (A)

A fixed point

Answer 2

Take two perpendicular lines as the coordinate axes. If a, b be the intercepts made by the moving line on the coordinate axes, then the equation of the line is

$\frac { x } { a } + \frac { y } { b } = 1$ .....(i)

According to the question

$\frac { 1 } { a } + \frac { 1 } { b } = \frac { 1 } { k }$, (say)

i.e.,$\frac { k } { a } + \frac { k } { b } = 1$ .....(ii)

The result (ii) shows that the straight line (i) passes through a fixed point (k, k).