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Manipal MET2013MathematicsStraight Lines

A straight line cuts intercepts from the axis of coordinates the sum of the reciprocals of which is a constant K . Then it always passes through a fixed point

Options

  1. A(K, K)
  2. B( 1 K , 1 K )
  3. C(-K,-K)
  4. D(K-1, K-1)

Correct answer

B. ( 1 K , 1 K )

Step-by-step solution

Let the equation of the line be x a + y b =1 ....(i) Its intercepts on y and x axes are b and a respectively. According to the question, 1 a + 1 b = constant =K 1 a + 1 b = constant =K (say) 1 a K + 1 b K =1 1 / K a + 1 / K h =1 ....(ii) From (ii) it follows that line (i) passes tnorougn the fixed point ( 1 K , 1 K ) .

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