0

Given a question to graph:

x^2 + 4y^2 = 16

I would assume its a 2D Plot. My textbook assumes otherwise and treats it as a trace.

enter image description here

This is how the equation looks like when plotted.

x^2 + 4y^2 = 16

enter image description here

My question is - is the 3D plot of x^2 + 4y^2 = 16 the same as the 2D plot of x^2 + 4y^2 = 16 except one is parallel to the plane and thats it? What distinguishes them? In the future if Im asked to draw a cylinder plane what would be the proper equation for it?

Álvaro Lozano-Robledo
  • 15,390
Sad CRUD Developer
  • 452
  • 1
    $z$ is arbitrary, so you just move up and down that ellipse along $z$ axis, and you get your elliptic cylinder. – Kaster Apr 01 '14 at 00:01
  • So x^2 + y^2 = 1 is a cylinder? – Sad CRUD Developer Apr 01 '14 at 00:03
  • I thought it would be x^2 + y^2 + z^1 = 1. But I forgot z is 0 – Sad CRUD Developer Apr 01 '14 at 00:08
  • what you wrote is sphere, not cylinder, and $z$ is not 0, its coefficient is zero. – Kaster Apr 01 '14 at 00:11
  • x^2+y^2 = 1 is a restriction on the values of x and y. There is no restriction on z, so this equation represents a cylinder with axis along the z axis. Similarly, z = 0 is the horizontal plane in 3D as the only restriction on (x, y, z) is that z = 0. The equation y = 0 would represent the horizontal axis in 2D too. – Paul Apr 01 '14 at 18:59

1 Answers1

1

$x^2+4y^2 = 16$ is the same thing as saying that $x^2+4y^2+0z=16$. So $z$ will not affect your graph, but now you can graph this equation in $3$ dimensions.

Sidd Singal
  • 3,452