Identify the type of quadric surface defined by the equation

$$3x^{2}+5y^{2}+z = 15,$$
and find all x-, y-, and z-intercepts of the resulting graph. Sketch the graph of this quadric surface on paper.

The quadric surface is a / an Choose elliptic cylinder hyperbolic cylinder parabolic cylinder elliptic paraboloid hyperbolic paraboloid ellipsoid hyperboloid of one sheet hyperboloid of two sheets elliptic cone with
x-intercepts when $x =$ ,
y-intercepts when $y =$ , and
z-intercepts when $z =$ .

Enter your answers as comma separated lists, or enter NONE if there are no intercepts of a particular type.