Question

Le kai

Answer 1

@Kainui ok so I have \[4x^2-y+2z^2=0\] how would I go about doing this using solids of revolution "method"

Answer 2

Is this capped off by a plane somewhere in the xz plane?

Answer 3

So the way I was taught for example, if we have \[x^2-y^2-z^2=1\]actually lets just focus on this one and I want to understand it :P
So first \[x^2-(y^2+z^2)=1\] starting with the hyperbola since it's \[x^2-y^2=1\] then I would rotate it about the x - axis \[r=z^2+y^2\]

Answer 4

Sure whatever you wanna do haha.

Answer 5

But I don't exactly understand why we rotate it about the x - axis haha

Answer 6

Since it's parallel or something?

Answer 7

i find this method confusing really haha, we weren't taught the cross sections really, so I'm sort of lost :P

Answer 8

Well the way I like to do it is just imagine each cutaway. Don't try to take one slice and then do something fancy with it, just take slices.

The hyperbola you chose is a specific one when z=0. You can change this to be anything though, pretend it gets absorbed into 1 as being an arbitrary constant maybe that will help. Best thing you can do right now is draw me the pictures of the 3 separate simplest cross sections: So far you've found the cross section when z=0, draw it and label your axes. Then repeat this two more times except let z be free again and make x or y be 0.

Answer 9

I'm not exactly sure how to draw it on the zy-plane alone, but xy it would be a hyperboloid sort of like this