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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