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JEE Main & Advanced Mathematics Straight Line Question Bank Distance between two lines, Perpendicular distance of the line from a point Position of point w.r.t. line

  • question_answer
    If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then  [Karnataka CET 2003]

    A)            \[{{a}^{2}}+{{b}^{2}}={{p}^{2}}\]                             

    B)            \[{{a}^{2}}+{{b}^{2}}=\frac{1}{{{p}^{2}}}\]

    C)            \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{2}{{{p}^{2}}}\]       

    D)            \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}\]

    Correct Answer: D

    Solution :

                \[p=\frac{ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\]  or \[\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}{{b}^{2}}}=\frac{1}{{{p}^{2}}}\Rightarrow \frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}\].


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