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

It is given that (x – a)^{2} + 2y^{2} = a^{2}

⇒ x2 + a2 – 2ax + 2y2 = a2

⇒ 2y2 = 2ax – x2 ---------(1)

Now, differentiating both sides w.r.t. x, we get,

- ---------(2)

So, equation (1), we get,

2ax = 2y^{2} + x^{2}

On substituting this value in equation (3), we get,

Therefore, the differential equation of the family of curves is given as .

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