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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 \[2p\] is the length of perpendicular from the origin to the lines \[\frac{x}{a}+\frac{y}{b}=1\], then \[{{a}^{2}},8{{p}^{2}},{{b}^{2}}\]are in

    A)            A. P.                                           

    B)            G.P.

    C)            H. P.

    D)            None of these

    Correct Answer: C

    Solution :

               We have \[2p=\left| \,\frac{0+0-1}{\sqrt{\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}}}\, \right|\Rightarrow \frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{4{{p}^{2}}}\]                    Þ  \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{2}{8{{p}^{2}}}\Rightarrow \frac{1}{{{a}^{2}}},\frac{1}{8{{p}^{2}}},\frac{1}{{{b}^{2}}}\]are in A. P.                    Þ  \[{{a}^{2}},8{{p}^{2}},{{p}^{2}}\]are in H.P .


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