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MHT CET2012MathematicsApplication of Derivatives

All the points on the curve y²=4 a|x+a (x / a)| , where the tangent is parallel to the axis of x are lies on

Options

  1. Acircle
  2. Bparabola
  3. Cstraight line
  4. DNone of these

Correct answer

B. parabola

Step-by-step solution

y²=4 a [x+a ( x a ) ] ...(i) 2 y d y d x =4 a [1+ ( x a ) ] ...(ii) If tangent is parallel to x -axis, then d y d x =0 So, from Eq. (i), we get ( x a )=-1 ( x a )=0 On putting this value in Eq. (i), we get y²=4 a(x+0) y²=4 a x So, all the points on the curve y²=4 a (x+a x a ) where the tangent is parallel to the x -axis are lies on parabola.

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