Find the differential equation of all the parabolas with latus rectum `4a` and whose axes are parallel to x-axis.

Explanation

Equation of the parabolas with lactus rectum `4a` and axis parallel to x-axis is,

`(y-beta)^2=4a(x-alpha) `

Differentiating it with respect to `x`, we get

`2(y-beta){dy}/{dx}=4aldots`(1)

Differentiating it with respect to `x`, we get

`(y-beta){d^2y}/{dx^2} +({dy}/{dx})^2=0 ldots`(2)

From (1) and (2),

`2a{d^2y}/{dx^2}+({dy}/{dx})^3=0`

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