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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer
    The equation of the normal to the curve \[\mathbf{y}=\mathbf{sinx}\] at \[\left( \mathbf{0},\mathbf{0} \right)\] is:

    A) \[x+y=0\]        

    B) \[x=y\]       

    C) \[x=0\]                         

    D) \[y=0\]

    Correct Answer: A

    Solution :

    [a] \[\therefore \]The equation of the curve is \[y=sin\text{ }x\]                         \[\therefore \frac{dy}{dx}=\cos x\]             \[{{\left. \frac{dy}{dx} \right|}_{at\,(0,0)}}=\cos 0=1\] \[\therefore \] Slope of the normal \[=-1\] So, the equation of the normal at (0, 0) be \[y-0=m\left( x-0 \right)\] \[\Rightarrow y=(-1)x\] \[\Rightarrow x+y=0.\] Hence, option [a] is correct.


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