Multivariable Calculus, plane sketching

[Twice]

How do I know where to put the axes for the equation 4x^2 - 9y^2 = z when graphing in 3d?

 

[fresh_42]

How do I know where to put the axes for the equation 4x^2 - 9y^2 = z when graphing in 3d?

That's up to you, which kind of projection you use. I always used

 

[Twice]

Thank you. Can you please explain to me how to sketch the plane on the axes?

 

[fresh_42]

Thank you. Can you please explain to me how to sketch the plane on the axes?

Which plane? You have a hyperbolic paraboloid there.

https://www.wolframalpha.com/input/?i=4x^2+-+9y^2+=+z

Planes are relatively easy to sketch. One uses the intersections with the "three walls" (x=0;y=0;z=0) to get an impression of a plane.

 

[Twice]

Which plane? You have a hyperbolic paraboloid there.
View attachment 233623
https://www.wolframalpha.com/input/?i=4x^2+-+9y^2+=+z

Planes are relatively easy to sketch. One uses the intersections with the "three walls" (x=0;y=0;z=0) to get an impression of a plane.

Right, thanks, I meant how do I draw the hyperbolic paraboloid on the axes?

 

[fresh_42]

Right, thanks, I meant how do I draw the hyperbolic paraboloid on the axes?

That's indeed not an easy task. I would start step by step along different values of $z$. Maybe you will need to change the order of the coordinates to improve the picture, but that can only be said after you saw what it looks like. The link above got you how it would look like and it's very curved. Maybe there are better graphic programs out there, but I don't know them. (Of course there are, but I meant the freely available ones.)

 

[Ray Vickson]

Right, thanks, I meant how do I draw the hyperbolic paraboloid on the axes?

You can use the free program "gnuplot", but it needs some getting used to. For some examples, see
https://www.google.ca/search?q=surf...eAhXI0J8KHTKeCKkQsAR6BAgGEAE&biw=1266&bih=589

In the meantime, here it is done using Maple (but that is not free).