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Form the differential equation representing family of curves given by (x - a)^2 + 2y^2 = a^2, where a is an arbitrary constant.

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Form the differential equation representing family of curves given by (x - a)2 + 2y2 = a2, where a is an arbitrary constant.

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Given equation of family of curves is

(x - a)2 + 2y2 = a2 .........(i)

On differentiating both sides w.r.t. x in Eq. (i), we get

On putting above value of a in Eq. (i), we get

Hence, the required differential equation is

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