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The differential equation of all circles passing through the origin and having their centres on the x-axis is

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The differential equation of all circles passing through the origin and having their centres on the x-axis is

(A) x2 = y2 + xy(dy/d)

(B) x2 = y2 + 3xy(dy/dx)

(C) y2 = x2 + 2xy(dy/dx)

(D) y2 = x2 - 2xy(dy/dx)

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Answer is (C) y2 = x2 + 2xy(dy/dx)

General equation of such circle is

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

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