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Find the differential equation of the family of a parabola with foci at the origin and axis along the x-axis.

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Find the differential equation of the family of a parabola with foci at the origin and axis along the x-axis.

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The equation of such family of parabolas is given by 

y2 = 4a(x + a) …… (1) 

Differentiating w.r.t x,

y = 2x(dy/dx) + y(dy/dx)2 is the differential equation.

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