In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y2 = a(b2 – x2)

The given equation is y2 = a(b2 – x2)

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

2yy’ = -2ax

yy’ = -ax -------(1)

Now, again differentiating both sides, we get,

y’.y’ +yy’’ = -a

(y’)2 + yy” = -a --------(2)

Now, dividing equation (2) by (1), we get,

xyy” + x(y’)2 – yy” = 0

Therefore, the required differential equation is xyy” + x(y’)2 – yy” = 0.

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