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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2007

  • question_answer
    The length of the sub tangent to the curve \[{{x}^{2}}{{y}^{2}}={{a}^{4}}\] at \[(-a,a)\] is

    A)  \[\frac{a}{2}\]                                  

    B)  \[2a\]

    C)  \[a\]                                    

    D)  \[\frac{a}{3}\]

    Correct Answer: C

    Solution :

    Given,/curve  \[{{x}^{2}}{{y}^{2}}={{a}^{4}}\] \[\Rightarrow \]                               \[{{y}^{2}}=\frac{{{a}^{4}}}{{{x}^{2}}}\] On differentiating, we get                 \[2y\frac{dy}{dx}=\frac{-2{{a}^{4}}}{{{x}^{3}}}\] \[\Rightarrow \]               \[\frac{dy}{dx}=\frac{-{{a}^{4}}}{{{x}^{3}}y}\] at            \[(-a,a),\frac{dy}{dx}=\frac{-{{a}^{4}}}{-{{a}^{3}}.a}=1\] Now, length of sub tangent to the given curve at \[(-a,a)\] is                                                             \[\frac{y}{dy/dx}=\frac{a}{1}=a\]


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