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
    The distance between the pair of parallel lines \[{{x}^{2}}+2xy+{{y}^{2}}-8ax-8ay-9{{a}^{2}}=0\] is  [Karnataka CET 2005]

    A)            \[2\sqrt{5}a\]                      

    B)            \[\sqrt{10}\,a\]

    C)            \[10\,a\]                                

    D)            \[5\sqrt{2}\,a\]

    Correct Answer: D

    Solution :

               Distance between parallel lines given by                    \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] is                    \[2\sqrt{\frac{{{g}^{2}}-ac}{a(a+b)}}\]\[=2\sqrt{\frac{{{(4a)}^{2}}+9{{a}^{2}}}{1(1+1)}}=2\sqrt{\frac{25{{a}^{2}}}{2}}=5\sqrt{2}a\].


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