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

  • question_answer
    The equation of the tangent at the point \[\left( \frac{a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}} \right)\] of the circle \[{{x}^{2}}+{{y}^{2}}=\frac{{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]is

    A)            \[\frac{x}{a}+\frac{y}{b}=1\]      

    B)            \[\frac{x}{a}+\frac{y}{b}+1=0\]

    C)            \[\frac{x}{a}-\frac{y}{b}=1\]

    D)            \[\frac{x}{a}-\frac{y}{b}+1=0\]

    Correct Answer: A

    Solution :

               From formula of tangent at a point,                    \[x\left( \frac{a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}} \right)+y\left( \frac{{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}} \right)=\frac{{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\Rightarrow \frac{x}{a}+\frac{y}{b}=1\].


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