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Problem 33 Medium Difficulty

Reduce the equation to one of the standard forms, classify the surface, and sketch it.

$ x^2 + 2y - 2z^2 = 0 $


hyperbolic paraboloid

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Video Transcript

All right. So you want to write access crap close to I minus studious cat ecology. Under standard form. So just moving my wife with the keeping by here and moving every other guy to the other side to get this a stogie square minor success. Where? So why is this where minus hard accessible. So so this is the question is industrial form. This is a hyperbolic parabolas. So the reason is the following as to why let's try to figure it out. So why is for us is G squared endoscopic Cisco. And let's try to draw the crabs. So for the sake of convenience, what I draw is this is my Y axis and this is my X. And you. So let's say that when Y is zero. So while I'm here this is this is really so this is why is zero. This is these criminals have access. So this is a pair of straight lines. Now let us look at what you call the one. So if what you call the one I'm here and then this is this permanent Have access for is one. So this is really why I called to one. This is a hyper bowl. This is a hyper book. What taxes is G index. So at why called one plane. This is this is something like like this. And then every time my wife increases this, this hyper bola. So if I look at, so this is something like but then it increases. So every point I'm just a hyper bola, Right? But this is a hyperbolic parabolas. The reason is to start every point for each value of why we get mhm hyper gola on the X. G.