The differential equation of the family of curves of `x^(2)+y^(2)-2ay=0` where a is arbitary constant, is
The differential equation of the family of curves of `x^(2)+y^(2)-2ay=0` where a is arbitary constant, is
A. `(x^(2)-y^(2))(dy)/(dx)=2xy`
B. `2(x^(2)+y^(2))(dy)/(dx)=xy`
C. `2(x^(2)-y^(2))(dy)/(dx)=xy`
D. `(x^(2)-y^(2))(dy)/(dx)=2xy`
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Given equation of curve is `x^(2)+y^(2)-2ay=0`
`Rightarrow (x^(2)+y^(2))/(y)=2a`
On differentiation both sides, w.r.t. we get
`(y(2x+2y(dy)/(dx))-(x^(2)+y^(2))(dy)/(dx))/(y^(2))=0`
`Rightarrow 2xy+2y^(2)(dy)/(dx)-(x^(2)+y^(2))(dy)/(dx)=0`
`Rightarrow (2y^(2)-x^(2)-y^(2))(dy)/(dx)=-2xy`
`Rightarrow (y^(2)-x^(2))(dy)/(dx)=-2xy`
`Rightarrow (x^(2)-y^(2))(dy)/(dx)=2xy`
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