JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    Let \[({{x}_{i}},{{y}_{i}})i=1,2,3,4\] are the integral solutions of equation \[2{{x}^{2}}{{y}^{2}}+{{y}^{2}}-6{{x}^{2}}-12=0.\] Then area of quadrilateral whose vertices are \[({{x}_{i}},{{y}_{i}})\]is

    A)  4                            

    B)  8       

    C)  12                         

    D)  16

    Correct Answer: D

    Solution :

    \[2{{x}^{2}}{{y}^{2}}+{{y}^{2}}-6{{x}^{2}}-12=0\Rightarrow (2{{x}^{2}}+1)({{y}^{2}}-3)=9\]\[\Rightarrow \]\[2{{x}^{2}}+1=\frac{9}{{{y}^{2}}-3}\Rightarrow y=\pm 2\And x=\pm 2\] \[\therefore \]vertices are \[(2,2),(2,-2),(-2,2)\And (-2,-2)\] Area = 16                                     

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