All points on the curve y2=4ax+asin⁡xa  at which the tangents are parallel to the axis of x lie on a

All points on the curve y2=4ax+asinxa  at which the tangents are parallel to the axis of x lie on a

  1. A

    circle 

  2. B

    parabola

  3. C

    line

  4. D

    none of these

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    Solution:

    We have, 

    y2=4ax+asinxa                                   ..(i)

     2ydydx=4a1+cosxa

    For points at which the tangents are parallel to x-axis, we must have

    dydx=04a1+cosxa=0cosxa=1xa=(2n+1)π

    For these values of x, we obtain sinxa=0

    Putting sinxa=0, in (i), we get y2=4ax

    Therefore, all these points lie on the parabola y2=4ax.

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