JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Critical Thinking

  • question_answer The product of perpendiculars drawn from the origin to the lines represented by the equation\[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\], will be  [Bihar CEE 1994]

    A)            \[\frac{ab}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}\]

    B)            \[\frac{bc}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}\]

    C)            \[\frac{ca}{\sqrt{({{a}^{2}}+{{b}^{2}})+4{{h}^{2}}}}\]           

    D)            \[\frac{c}{\sqrt{{{(a-b)}^{2}}+4{{h}^{2}}}}\]

    Correct Answer: D

    Solution :

               The product of perpendiculars\[=\frac{c}{\sqrt{{{(a-b)}^{2}}+4{{h}^{2}}}}\].

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