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  • Find the diffrential equation of all parabolas whose axis is parallel to the x-axis and having latus rectum a.

Find the diffrential equation of all parabolas whose axis is parallel to the x-axis and having latus rectum a.

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Solution:   Equation of parabola whose axis is parallel to x-axis

             and having latus rectum a. is

            (y-eta )^2=a(x-alpha )

           Diffrentiating both sides , we get   2(y-eta )fracmathrmd ymathrmd x=a

          Again diffrentiating  , we get

      Rightarrow   2(y-eta )fracmathrmd ^2ymathrmd x^2+2(fracmathrmd ymathrmd x)^2=0

   Rightarrow    afracmathrmd ^2ymathrmd x^2+2(fracmathrmd ymathrmd x)^3=0

 

Posted by

Deependra Verma

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