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

  • question_answer
    Which of the following lines is a tangent to the circle \[{{x}^{2}}+{{y}^{2}}=25\]for all values of m

    A)            \[y=mx+25\sqrt{1+{{m}^{2}}}\]                                        

    B)            \[y=mx+5\sqrt{1+{{m}^{2}}}\]

    C)            \[y=mx+25\sqrt{1-{{m}^{2}}}\]                                          

    D)            \[y=mx+5\sqrt{1-{{m}^{2}}}\]

    Correct Answer: B

    Solution :

               Line \[y=mx+c\] is a tangent if \[c=\pm a\sqrt{1+{{m}^{2}}}\]                    \[\therefore \]\[y=mx+5\sqrt{1+{{m}^{2}}}\].


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