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

Explanation

(i) ` x^2+y^2=a^2 `

Differentiating it with respect to `x`, we get

`2x+2y{dy}/{dx}=0`

`implies x+y{dy}/{dx}=0`

This is the required differential equation.

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

Differentiating it with respect to `x`, we get

`2x-2y{dy}/{dx}=0`

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