Family of curves: parabola?

Can you please help me understand the steps in finding the differential equation for parabolas whose vertex are on the y axis and with fixed focal distance a.

Someone said it is a parabolic PARTIAL DIFF EQ. But I dont know what that means

1 Answer

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  • 1 month ago

    If the parabola is of the form y^2 = 4ax 

    Then the differential is 

    2ydy/dx = 4a 

    dy/dx = 4a / 2y  = 2a / y 

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