The curve satisfying $y=2 x \frac{d y}{d x}$ is a :

family of parabola family of circle pair of straight line none of these

family of parabola

$\frac{d x}{d y}=\frac{2 d y}{y} \Rightarrow \ln y=\ln y^2+\ln c \Rightarrow y^2=kx$ it represents a family of parabola Hence (1) is the correct answer.