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JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    The distance between the origin and the normal to the curve \[y={{e}^{2x}}+{{x}^{2}}\] at \[x=0\], is

    A)  \[\frac{1}{\sqrt{5}}\]                                    

    B)  \[\frac{2}{\sqrt{5}}\]

    C)  \[\frac{2}{\sqrt{3}}\]                                    

    D)  \[\frac{1}{2}\]

    Correct Answer: B

    Solution :

    \[y={{e}^{2x}}\,+{{x}^{2}}\]             At, \[x=0,\,\,y=1\]             Now, \[{{\left. \frac{dy}{dx} \right]}_{(0,1)}}\,=2{{e}^{2x}}\,+2x=2\] \[\therefore \] Equation of normal at (0, 1) is \[\therefore \,\,\,(y-1)\,=\frac{1}{2}\,(x-0)\,\,\Rightarrow \,x+2y-2=0\] So, required distance from (0, 0) is \[=\frac{|0+0-2|}{\sqrt{5}}\,=\frac{2}{\sqrt{5}}\]


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