Identifying Quadric Surfaces: Memorization or Visualization?

[magic88]

Hi there,

I am learning about quadric surfaces in my second year multivariable calculus course.

I would like to know how most people would identify (find the name of) a quadric surface if they had the equation. We only need to know 6 different quadric surfaces, so should I ...

(a) memorize the equations to identify the surface, or
(b) sketch out what the xy-, xz-, and yz-planes look like, sketch out the surface to see what it looks like, then identify it?

What do you do?

Thanks in advance.

 

[fresh_42]

I would look it up or normalize them if needed. Nowadays with tools like WolframAlpha you can even plot them easily. In case you need it for an exam, you should ask your teacher.