The first order differential equation of the family of circles with fixed radius $r$ and with centre on $x$ -axis is:

y^{2} (\frac{d y}{d x})^{2} + y^{2} = r^{2}

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x^{2} (\frac{d y}{d x})^{2} + y^{2} = r^{2}

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(\frac{d y}{d x})^{2} + y^{2} = r^{2}

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y^{2} - (\frac{d y}{d x})^{2} = r^{2}

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Solution

The correct option is B $y^{2} (\frac{d y}{d x})^{2} + y^{2} = r^{2}$
$\Rightarrow (x - a)^{2} + y^{2} = r^{2}$
$\Rightarrow 2 (x - a) + 2 y y_{1} = 0$
$\Rightarrow (x - a) = - y y_{1}$
$\Rightarrow y^{2} y_{1}^{2} + y^{2} = r^{2}$

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The first order differential equation of the family of circles with fixed radius r and with centre on x -axis is:

The correct option is B y2(dydx)2+y2=r2⇒(x−a)2+y2=r2⇒2(x−a)+2yy1=0⇒(x−a)=−yy1⇒y2y21+y2=r2

The first order differential equation of the family of circles with fixed radius $r$ and with centre on $x$ -axis is:

The correct option is B $y^{2} (\frac{d y}{d x})^{2} + y^{2} = r^{2}$
$\Rightarrow (x - a)^{2} + y^{2} = r^{2}$
$\Rightarrow 2 (x - a) + 2 y y_{1} = 0$
$\Rightarrow (x - a) = - y y_{1}$
$\Rightarrow y^{2} y_{1}^{2} + y^{2} = r^{2}$