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JCECE Engineering JCECE Engineering Solved Paper-2012

  • question_answer
    If the lines represented by \[{{x}^{2}}-2pxy-{{y}^{2}}\] are rotated about the origin through an angle\[\theta \], one in clockwise direction and other in anti-clockwise direction. Then, die equation of bisectors of the angles between the lines in the new position is

    A) \[p{{x}^{2}}+2xy+p{{y}^{2}}=0\]

    B) \[p{{x}^{2}}-2xy+p{{y}^{2}}=0\]

    C) \[p{{x}^{2}}+2xy-p{{y}^{2}}=0\]

    D)  None of these

    Correct Answer: C

    Solution :

    The bisectors of the angles between the lines in the new position are same as the bisectors of the angles between their old positions. Therefore, required equation is                 \[\frac{{{x}^{2}}-{{y}^{2}}}{1-(-1)}=\frac{xy}{-p}\] \[\Rightarrow \]               \[-p{{x}^{2}}+p{{y}^{2}}=2xy\] \[\Rightarrow \]               \[p{{x}^{2}}+2xy-p{{y}^{2}}=0\]


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