💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

TA

# (a) Find and identify the traces of the quadric surface $x^2 + y^2 - z^2 = 1$ and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1.(b) If we change the equation in part (a) to $x^2 - y^2 + z^2 = 1$, how is the graph affected?(c) What if we change the equation in part (a) to $x^2 + y^2 + 2y - z^2 = 0$?

## a) The $z=k$ traces are circles, the $x=k$ and $y=k$ traces are hyperbolas.b) The $y$ -axis becomes the axis of symmetry. The $y=k$ traces become the ones with the circles while the $x=k, z=k$ traces are hyperbolas.c) The center moves from $(0,0,0)$ to $(0,-1,0)$

Vectors

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp

### Video Transcript

No transcript available

#### Topics

Vectors

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp