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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Tangent and normal to a circle

  • question_answer
    If the line \[lx+my=1\]be a tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then the locus of the point (l, m) is [MNR 1978; RPET 1997]

    A)            A straight line                           

    B)            A Circle

    C)            A parabola                               

    D)            An ellipse

    Correct Answer: B

    Solution :

               If the line \[lx+my-1=0\] touches the circle\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then applying the condition of tangency, we have \[\pm \frac{l.0+m.0-1}{\sqrt{{{l}^{2}}+{{m}^{2}}}}=a\]                    On squaring and simplifying, we get the required locus \[{{x}^{2}}+{{y}^{2}}=\frac{1}{{{a}^{2}}}\]. Hence it is a circle.


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