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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    If locus of a point, whose chord of contact with respect to the circle\[{{x}^{2}}+{{y}^{2}}=4\]is a tangent to the hyperbola\[xy=1\]is\[xy={{c}^{2}}\], then value of\[{{c}^{2}}\] is

    A)  2                            

    B)  4

    C)  1/2                       

    D)  1/4

    Correct Answer: B

    Solution :

     Let the point be (h, k). Then equation of the chord of contact is \[hx+ky=4\] since \[hx+ky=4\]is tangent to\[xy=1\] \[\therefore \] \[x\left( \frac{4-hx}{k} \right)=1\]has two equal roots i.e. \[h{{x}^{2}}-4x+k=0\] i.e. \[hk=4\] \[\therefore \]  locus of (h, k) is\[xy=4\] i.e., \[{{c}^{2}}=4\]


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