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

  • question_answer
    The equations of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}=36\]which are inclined at an angle of \[{{45}^{o}}\]to the x-axis are

    A)            \[x+y=\pm \sqrt{6}\]             

    B)            \[x=y\pm 3\sqrt{2}\]

    C)            \[y=x\pm 6\sqrt{2}\]              

    D)            None of these

    Correct Answer: C

    Solution :

               \[y=mx+c\] is a tangent, if \[c=\pm a\sqrt{1+{{m}^{2}}}\], where \[m=\tan {{45}^{o}}=1\]                    \[\therefore \ \]The equation is\[y=x\pm 6\sqrt{2}\].


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