The differential equation of all parabolas whose axis are parallel to the y-axis is

Explanation

`Equation of parabola is ({x}-{h})^{2}=4 {a}({y}-{k})`


Differentiating the equation with respect to x,


`Rightarrow 2(x-h)=4 ay_{1}`


`Rightarrow(x-h)=2 ay_{1}`


`Rightarrow 1=2 ay_{2}`


`Rightarrow y_{2}=frac{1}{2 {a}}`


Differentiating equation with respect to x,


`Rightarrow y_{3}=0`


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