Form the differential equation of the family of curves x^2+y^2-2ay=0
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first you differentiate this equation w.r.t x
2x+2y.dy/dx-2a.dy/dx=0
x+y.dy/dx-a.dy/dx=0-----(1)
from equation
x^2+y^2-2ay =0
a=(x^2+y^2)/2y put this value of a in (1)
x+y.dy/dx-(x^2+y^2)/2y.dy/dx=0
2x+2y.dy/dx-2a.dy/dx=0
x+y.dy/dx-a.dy/dx=0-----(1)
from equation
x^2+y^2-2ay =0
a=(x^2+y^2)/2y put this value of a in (1)
x+y.dy/dx-(x^2+y^2)/2y.dy/dx=0
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