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JEE Main & Advanced Sample Paper JEE Main Sample Paper-23

  • question_answer
    If the circle \[{{x}^{2}}+{{y}^{2}}-2x-4y+k=0\] and  director circle of ellipse \[\frac{{{x}^{4}}}{4}+{{y}^{2}}=1\] intersects orthogonally then k equals

    A)  0                    

    B)  5

    C)  \[-5\]                           

    D)  2

    Correct Answer: B

    Solution :

    Equation of director circle of ellipse\[\frac{{{x}^{2}}}{4}\,+{{y}^{2}}=1\,\] is \[{{x}^{2}}+{{y}^{2}}=5\] or \[{{x}^{2}}+{{y}^{2}}-5=0\]                        ?(1) If above circle in equation (1) intersects orthogonally the circle \[{{x}^{2}}+{{y}^{2}}\,-2x-4y+k=0,\] then \[k-5=0\Rightarrow \,k=5\] (Using condition of orthogonality of two circle)


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