Sketching Surfaces: Sphere, Circle & More

[sheepcountme]

Homework Statement

I'm also having trouble with these:

provide the names and sketch the following surfaces:
x²+y²+z²=16
x²+y²=9
x²+2y²+4z²=16
z=-√(9-x²-y²)
z=√x²+y²
z=x²+y²

Homework Equations

The Attempt at a Solution

So for the first one it's a sphere with radius of 4, yes? And the second is a circle with radius three. These seem fairly obvious but I'm not sure how to go about visualizing the rest...is this something I just need to pick up on or is there a method I should be using?

 

[lanedance]

once again taking cuts is good

for 3) this looks like a sphere squashed along certain axes

take z=0, this give
x^2+2y2=16
at y=0, x=4
at x=0, y=2sqrt(2)

which is an oval, once again try sketching it

 

[LCKurtz]

Homework Statement

I'm also having trouble with these:

provide the names and sketch the following surfaces:
x²+y²+z²=16
x²+y²=9
x²+2y²+4z²=16
z=-√(9-x²-y²)
z=√x²+y²
z=x²+y²

Homework Equations

The Attempt at a Solution

So for the first one it's a sphere with radius of 4, yes? And the second is a circle with radius three.

A circle isn't a surface. The trace of this surface in the xy plane is a circle. In fact in the plane z = any constant its trace is a circle. So the surface itself is a circular cylinder. This is typical of equations that have a missing variable. The trace projects itself in the direction of the missing variable.

These seem fairly obvious but I'm not sure how to go about visualizing the rest...is this something I just need to pick up on or is there a method I should be using?

Often all you need to do is draw the traces in the coordinate planes and sometimes one or two other planes to get an idea what the surface looks like. For example, for your last one the traces in the z-x and z-y planes are parabolas and the trace in the z = 4 plane is a circle. So...

 

[lanedance]

good points