Question

how to plot \[x^2 + y^2 - z^2 = 16\] in x,y,x plane?

Answer 1

http://www.wolframalpha.com/input/?i=x%5E2%2By%5E2-z%5E2%3D16

Answer 2

@agent0smith how to plot it in x, y plane?

Answer 3

It's a 3d graph, you'd have to choose a cross section if you want a 2D view :/

Answer 4

ah ok will you teach me the step by step procedure on how to graph this?

Answer 5

I guess if you're just looking at the x y plane then it's a hyperbola... but you're trying to put a 3D graph on a 2D image.

Answer 6

ah ok will u guide me in sketching this?

Answer 7

I don't know exactly how to sketch this particular graph in the 2D plane, but the general shape will be like: http://intmstat.com/plane-analytic-geometry/hyperbola-6.gif

Answer 8

you know how to sketch in 3D? will you teach me?

Answer 9

No, i don't know how to sketch in 3d really, except for more obvious equations like spheres.

Answer 10

ah ok tnx

Answer 11

In general, you want to create a table of x and y value combinations, then have the other side be the z value

Answer 12

That's how you graph simpler \(z=f(x,y)\) functions.

Answer 13

You have to have experience to just recognized many of the 3D common shapes, like cones, ellipsoids, spheres, etc.

Answer 14

x2+y2−z2=16 can you guide me in graphing this in x,y,z plane?

Answer 15

Okay, well if you mess around with the equation, you get: \[
z^2 = x^2+y^2+16
\]

Answer 16

This is just \[
z^2=x^2+y^2
\]shifted up the \(z\) axis by \(16\)

Answer 17

Notice that if you set \(z\) to be a constant... suppose \(z=k\)...
We get \[
k = x^2+y^2
\]which is the equation of a circle, radius \(\sqrt{k}\)

Answer 18

So each cross section along the z axis is going to be a circle:

Answer 19

Since it is symmetric about the \(z\) axis, we can just look at the \(xz\) plane and rotate that result around the \(z\) axis.

Answer 20

Looking at the \(xz\) plane (do this by letting \(y=0\)) gets us the equation\[
z= x^2+16
\]

Answer 21

Rotating this about the \(z\) axis gives us: