Represent the following families of curves by forming the corresponding differential equations (a, b being parameters): (i) `y^2=4a x` (ii) `y^2=4a(x-b)`

Explanation

(i) `y^2=4a xldots `(1)

Differentiating it with respect to `x`, we get

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

Eliminating `a` from (1) and (2), we get
`implies y-2x{dy}/{dx}=0`

This is the required differential equation.

(ii)` y^2=4a(x-b)`

Differentiating it with respect to `x`, we get

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