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

Like

Report

Numerade Educator

Like

Report

Problem 30 Medium Difficulty

Sketch and identify a quadric surface that could have the traces shown.

Traces in $ x = k $
Traces in $ z = k $

Answer

This is a one-sheeted hyperboloid

More Answers

Discussion

You must be signed in to discuss.

Video Transcript

So, um, for this problem, we want to look at when x is constant. When x is constant, we see we get the equation of the form P Y squared plus Q Z squared equals one. Lindsay is constant. We get something of the form M X squared minus and Y squared equals one. And therefore we have an equation of the surface that's of the form a X squared minus B y squared plus C Z squared equals one, and that's going to be a one sheeted hyperba, Lloyd. So the way we make sense of this is if we have, um, our Z axis and then we have the Y axis, and then we have our X axis. What we end up seeing is that this sheet will be in such a way that it opens up here, and then it kind of has this hourglass shaped like this. So that would be our one sheeted hyper Boyd