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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

  • question_answer
    Distance between the pair of lines represented by the equation \[{{x}^{2}}-6xy+9{{y}^{2}}+3x-9y-4=0\]is  [Kerala (Engg,) 2002]

    A)            \[\frac{15}{\sqrt{10}}\]    

    B)            \[\frac{1}{2}\]

    C)            \[\sqrt{\frac{5}{2}}\]        

    D)            \[\frac{1}{\sqrt{10}}\]

    Correct Answer: C

    Solution :

               The distance between the pair of straight lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] is \[2\sqrt{\frac{{{g}^{2}}-ac}{a(a+b)}}\].                    Here \[a=1,\,\,b=9\]Þ \[c=-4,\,\,g=3/2\]            = \[2\times \sqrt{\frac{9/4-(-4)}{1(1+9)}}=2\times \sqrt{\frac{25/4}{10}}\] = \[\sqrt{5/2}\].


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