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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    If the curves \[{{x}^{2}}-{{y}^{2}}=4\]and \[xy=\sqrt{5}\]intersect at points A and 5, then the possible number of point(s) C on the curve \[{{x}^{2}}-{{y}^{2}}=4\]such that triangle ABC is equilateral is

    A)  0                                            

    B)  1

    C)  2                                            

    D)  4

    Correct Answer: A

    Solution :

     A and B are \[(\sqrt{5},1)\] and\[(-\sqrt{5},-1).\] Let C be \[(2sec\theta ,2tan\theta ).\] \[O(0,0)\]is the mid point of AB. Slope of \[OC=\sin \theta \]and slope of \[AB=\frac{1}{\sqrt{5}}\] Since \[OC\bot AB.\] \[\sin \theta =-\sqrt{5}\]which is impossible.


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