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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    The parabola \[{{y}^{2}}=4ax\] and the circle \[{{x}^{2}}+{{y}^{2}}+2bx=0\] have more than one common tangents, if

    A)  \[ab<0\]                             

    B)  \[ab>0\]

    C)  \[ab<-1\]                           

    D)  \[ab<-2\]

    Correct Answer: B

    Solution :

    \[\because \] Both parabola and circle pass through origin. The equation of circle can be written as\[{{(x+b)}^{2}}+{{y}^{2}}={{b}^{2}}\]. For more than one common tangents, the focus \[(a,\,0)\] and the centre (-b, 0) should lie on opposite side of origin. \[\therefore \,\,a(-b)<0\Rightarrow ab>0\]


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