Question

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

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

Answer 1

The correct option is A $x^2-y^2+2xy\frac{dy}{dx}=0$

$(x-4{)}^2+y^2=y^2$
$\Rightarrow 2(x-4)+2y{y}_1=0$
$\Rightarrow (x-4)-y{y}_1$
$4=x+y{y}_1$
$\Rightarrow y^2{y}_1^2+y^2=x^2+y^2{y}_1^2+2xy{y}_1$
$\Rightarrow x^2-y^2+2xy\frac{dy}{dx}=0$