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Problem 36 Medium Difficulty

Reduce the equation to one of the standard forms, classify the surface, and sketch it.
$ x^2 - y^2 - z^2 - 4x - 2z + 3 = 0 $


Standard form: $(x-2)^{2}-y^{2}-(z+1)^{2}=0$
This is an infinite cone

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Video Transcript

So you want to write this in the standard form again? So again, we'll just keep the like, like comes together to access criminals forex. So the question again, Right, this is correct. Yeah, can you complete the square? This is the square when it's two times two weeks last school square Venezuela scary escape tragedies. And then G square lost two key last one, first three since I've already to spread here and then I've subtracted one here. This one. So This is X -2 square minus y. Square. Finance G -1 sq is exactly what? So what you get is that experience to square is why squared There's AG -1 suppression. Yes, she just started for mhm. Mhm. And how do we try it? Okay, So for convenience, what I'll do is I'll draw this as my success and this is my wife. Yeah. Right. Yeah. Thanks. And the question that we want to figure out his expenses to square advice square, So I can't remember this. 34 access to. Right, So what offenses that at every point I get a circle of certain parties. But so and the radius changes. Right? So let's say if access to who is here then I get y squared plus G minus one squared zero. This means that y zero Gs exactly called. So this means that exactly equal to two. I'm really intercepting the bye. Mhm. So access to this means that why is zero sum 10 So really I'm indeed XG plenty. And then her next is zero and get a circle. So basically every time I circle my point is centered at 1:00. You know what this is where my circle isn't. And then I the search radius varies depending on where I am. So for example, if I am at a zero, if my excess Jiro then my circle radius is too. So this is the original one, then my second oldest sister, something like this has happened basically. What is happening is that every time my ex values from here to there Then effects is three. Then again I get so it is decreasing. Oppress certain point, right? So really it's just like an infinite call like this. So for a certain point it comes down and it egregious tries to decrease and then it reads disappoint of this and then it goes increasing it. So every time like this circle, my center is the same circle, the center of the circle is the same, but my radius increases, the radius is increasing really.