Form the differential equation of the family of curves represented by the equation (a being the parameter):

i. (2x + a)2 + y2 = a2


ii. (2x – a)2 – y2 = a2


iii. (x – a)2 + 2y2 = a2

(i)

(2 x + a)2 + y2 = a2


On differentiating, with respect to x we have,





Putting this value of a in the given equation we get,





ii. (2 x – a)2 – y2 = a2


⇒ 4x2 + a2 – 4ax – y2 = a2


⇒ 4x2 – 4ax – y2 = 0


⇒ 4ax = 4x2 – y2



On differentiating with respect to x we get,





iii. (x – a)2 + 2 y2 = a2


On differentiating, with respect to x we have,





Putting this value of a in the given equation we get,





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