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  • The differential equation of the family of ellipse having major and minor axes respectively along the x and y axis and the minor axis is equal to half of the major axis is

The differential equation of the family of ellipse having major and minor axes respectively along the x and y axis and the minor axis is equal to half of the major axis is

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Solution:     Equation of the given family of ellipse is 

                                         fracx^24a^2+fracx^2a^2=1

                  Rightarrow            x^2+4y^2=4a^2             ........(1)

                  Differentiating  w.r.to x  , we get 

                                   2x+8yfracmathrmd ymathrmd x=0Rightarrow x+4yfracmathrmd ymathrmd x=0.   

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Deependra Verma

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