Calc AB question: quite simple?

Question

At each point (x,y) on a certain curve, the slope of the curve is 2y/x, then the curve is a:

straight line
parabola
circle
ellipse
hyperbola

why?

Answer 1

the gradient is the slope
that is
dy/dx = 2y/x
dy/y = 2dx/x
ln(y) = 2ln(x) +C
ln(y) = ln(x^2) +C
y = x^2 +C

parabola

Answer 2

dy/dx = 2y/x
so
dy/y =2 dx/x
lnIyI= 2lnIxI+ K
so
y=C*x^2 which is an parabola