Solving Review Problems: Intersections of 3D Equations Explained

[sheepcountme]

Homework Statement

I'm having some trouble remembering how to do this in a refresher course...

sketch the intersection of (x^2)+(y^2)+(z^2)=3 and z<0
sketch the intersection of z=2(x^2)+2(y^2) and z=4-(x^2)-(y^2)

Homework Equations

The Attempt at a Solution

I think the first one is a circle with points at 1 and -1 on each axis, not too sure if there's a certain method I'm supposed to use to figure this out with though.

 

[lanedance]

note quite... the first is the half the surface of a sphere below zero

one way that may help is too look at the intesection with a plane (x=0,y=0,z=0) are good

then you either need to recognise the form or think about how one viarable relates toteh other the other

eg. for 2)
z=2(x^2)+2(y^2)

x=0
z=2(y^2)

x=0
z=2(x^2)

these are both idenitical parabolas

z=c>0
c/2=(x^2)+(y^2)

cuts in the cy planes give circles, so this a circular paraboloid,

you should try drawing each of the parbaolas and a circle in 3D perspective on paper