2. Solved Papers
  3. Manipal Engineering

Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    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

    A) \[(K,\,\,K)\]                       

    B) \[\left( \frac{1}{K},\,\,\frac{1}{K} \right)\]

    C) \[(-K,\,\,-K)\]    

    D)        \[(K-1,\,\,K-1)\]

    Correct Answer: B

    Solution :

    Let the equation of the line be\[\frac{x}{a}+\frac{y}{b}=1\]         ... (i) Its intercepts on\[y\]and\[x\]axes are\[b\]and\[a\]respectively. According to the question,                 \[\frac{1}{a}+\frac{1}{b}=\]constant\[=K\](say) \[\therefore \]  \[\frac{1}{aK}+\frac{1}{bK}=1\] \[\Rightarrow \]               \[\frac{1/K}{a}+\frac{1/K}{b}=1\]                                             ... (ii) From (ii) it follows that line (i) passes through the fixed point\[\left( \frac{1}{K},\,\,\frac{1}{K} \right)\].


You need to login to perform this action.
You will be redirected in 3 sec spinner