Represent the following families of curves by forming the corresponding differential equations (a, b being parameters): (i) `x^2+(y-b)^2=1` (ii) `y=a x^3`

Explanation

(i) ` x^2+(y-b)^2=1ldots `(1)

Differentiating it with respect to `x`, we get

`2x+2(y-b){dy}/{dx}=0ldots`(2)

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

This is the required differential equation.

(ii)` y=ax^3ldots`(1)

Differentiating it with respect to `x`, we get

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