JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    Number of ordered pairs \[(x,y)\] satisfying the equation \[4{{y}^{2}}+2{{\cos }^{2}}x=4y-{{\sin }^{2}}x\], where \[x,y\in [0,2\pi ]\], is

    A)  1                     

    B)  2

    C)  3                                

    D)  4

    Correct Answer: B

    Solution :

    Given, \[4{{y}^{2}}+2{{\cos }^{2}}x=4y-{{\sin }^{2}}x\] \[\Rightarrow \,4{{y}^{2}}-4y+1+{{\cos }^{2}}x=0\] \[\Rightarrow \,{{(2y-1)}^{2}}+{{\cos }^{2}}x=0\] \[\therefore \,\,y=\frac{1}{2}\,\,and\,\,x=0\Rightarrow \,x=\frac{\pi }{2},\,\frac{3\pi }{2}\] So, two ordered pairs are possible i.e., \[\left( \frac{\pi }{2},\,\frac{1}{2} \right)\] and \[\left( \frac{3\pi }{2},\,\frac{1}{2} \right)\]

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