Question

The differential equation of all circles passing through the origin and having their centres on the x-axis is $y^2=x^2+Kxy\frac{dy}{dx}$ then value of $K$ is

• A. $1$
• B. $2$
• C. $4$
• D. $6$

Answer 1

The correct option is B $2$

Let the centre be $(h,0)⟹(x-h{)}^2+(y{)}^2=h^2⟹x^2+y^2=2xh⟹y\frac{dy}{dx}=h-x$

$2h-x=x-kx+kh⟹k=2$