Question

The differential equation of the family of circles whose centre lie on x-axis and passing through origin is

Answer 1

Equation $\Rightarrow {(x-h)}^2+y^2=h^2$

$x^2+y^2+h^2-2hx=h^2$

$x^2+y^2-2hx=0$

$2x+2y\frac{dy}{dx}-2h=0$

$h=x+y\frac{dy}{dx}$

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

$x^2+y^2-2x^2-2xy\frac{dy}{dx}=0$

$y^2-x^2-2xy\frac{dy}{dx}=0$