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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    The length of the subtangent to the curve\[{{x}^{2}}+xy+{{y}^{2}}=7\]at\[(1,-3)\]is:

    A)  3                                            

    B)  5

    C)  \[\frac{3}{5}\]                  

    D)         15         

    E)  4

    Correct Answer: D

    Solution :

    Given curve is \[{{x}^{2}}+xy+{{y}^{2}}=7\] On differentiating w.r.t.\[x,\] \[\Rightarrow \]\[2x+x\frac{dy}{dx}+y+2y\frac{dy}{dx}=0\] \[\Rightarrow \]               \[(x+2y)\frac{dy}{dx}=-(2x+y)\] \[\Rightarrow \]\[{{\left( \frac{dy}{dx} \right)}_{(1,-3)}}=\frac{-(2-3)}{(1-6)}=-\frac{1}{5}\] \[\therefore \]Length of subtangent\[=\frac{y}{\frac{dy}{dx}}=\frac{-3}{\frac{1}{-5}}=15\]


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