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

  • question_answer
    The gradient of the tangent line at the point \[(a\cos \alpha ,a\sin \alpha )\]to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], is

    A)            \[\tan \alpha \]                          

    B)            \[\tan (\pi -\alpha )\]

    C)            \[\cot \alpha \]                           

    D)            \[-\cot \alpha \]

    Correct Answer: D

    Solution :

               Equation of a tangent at \[(a\cos \alpha ,\ a\sin \alpha )\] to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] is \[ax\cos \alpha +ay\sin \alpha ={{a}^{2}}\].                    Hence its gradient is\[-\frac{a\cos \alpha }{a\sin \alpha }=-\cot \alpha \].


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