DE of all circles touching the Y-axis at the origin with centres on the X-axis

1. A.
   $\left(x+y\frac{dy}{dx}\right)^2 x^2=\left(x^2+y^2\right)^2$ (with factor 4 in numerator)
2. B.
   $\left(x+y\frac{dy}{dx}\right)^2 x^2=\left(x^2+y^2\right)^2$
3. C.
   $2\left(x+y\frac{dy}{dx}\right)^2 x^2=\left(x^2+y^2\right)^2$
4. D.
   $\left(x+y\frac{dy}{dx}\right)^2 x^2=4\left(x^2+y^2\right)^2$

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1. A.
   $y^2=x^2+xy\dfrac{dy}{dx}$
2. B.
   $x^2=y^2+2xy\dfrac{dy}{dx}$
3. C.
   $y^2=x^2+2xy\dfrac{dy}{dx}$
4. D.
   $x^2=y^2-xy\dfrac{dy}{dx}$

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1. A.
   $x^{2} + y^{2} + 2xy\frac{\text{ }dy}{\text{ }dx} = 0$
2. B.
   $x^{2} - y^{2} + 2xy\frac{\text{ }dy}{\text{ }dx} = 0$
3. C.
   $\ 2x^{2} + y^{2} + xy\frac{\text{ }dy}{\text{ }dx} = 0$
4. D.
   $\ x^{2} - 2y^{2} + 2xy\frac{\text{ }dy}{\text{ }dx} = 0$

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