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JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation of implicit function Parametric

  • question_answer
    If \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\], then \[\frac{dy}{dx}=\]

    A)            \[-\frac{ax+hy+g}{hx-by+f}\]

    B)            \[\frac{ax+hy+g}{hx-by+f}\]

    C)            \[\frac{ax-hy-g}{hx-by-f}\]

    D)            None of these

    Correct Answer: A

    Solution :

               \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\]            Differentiating w.r.t. x of y, we get            \[2ax+2h\left( y+x\frac{dy}{dx} \right)+2by\frac{dy}{dx}+2g+2f\frac{dy}{dx}=0\]                    \[\therefore \frac{dy}{dx}(2hx+2by+2f)=-(2ax+2hy+2g)\]                    or                                       \[\frac{dy}{dx}=-\frac{(ax+hy+g)}{(hx+by+f)}\].


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