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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 40

  • question_answer
    The line \[y=mx\]intersects the circles \[{{x}^{2}}+{{y}^{2}}-2x-2y=0\]and \[{{x}^{2}}+{{y}^{2}}+6x-8y=0\]at points A and B, respectively, (points being other than origin). The range of m such that origin divides AB internally is

    A) \[-1<m<\frac{3}{4}\]

    B)        \[m>\frac{4}{3}\] or \[m<-2\]

    C) \[-2<m<\frac{4}{3}\]

    D) \[m>-1\]

    Correct Answer: A

    Solution :

    [a] The tangents at the origin to \[{{C}_{1}}\] and \[{{C}_{2}}\] are \[x+y=0\]and \[3x-4y=0,\]respectively. Slopes of the tangents are \[-1\] and \[\frac{3}{4},\] respectively. Thus, if \[-1<m<\frac{3}{4}\]then origin divides AB internally.


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