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Numerade Educator

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Problem 15 Easy Difficulty

Use traces to sketch and identify the surface.

$ 9y^2 + 4z^2 = x^2 + 36 $

Answer

hyperboloid of one sheet

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Video Transcript

So what do you want to do is we want to draw the graph access square? Lost 36 equals to nine y square The last four G school. No, you observed one thing first start with the stress of case. So if X equals to stress effects in Mexico. Okay. We obtain okay squared plus 36 equals to nine Y square Plus four G square. This is an ellipse. Now if what he wants to. Okay. Mhm. We obtained that Excess Square -4 G sq Because nine K sq- Statistics. Which is in hi Pamela. And then if G equals to care we obtain that excess square minus nine Y squared equals to four K square minus 36 which is a hyperbolic. So Table one. It follows a decision. Hyperbolic of 16 How do we draw this graph? That is something that we want to figure out. So what I will do is I will draw the sun along the X axis. So let me do that. So what what we know is that access where we want to draw this graph? So first we observed that if I choose any value of X, this is an ellipse. So at every point I really get an ellipse. Yeah. So and the effect is you know I'm on the lips at the X. Y. Plane. So let me draw this is my ex thing, this is lying why by G. So I made out of business by why so much and this is my ex. So if X equals to zero, I'm here on the plane and I get an ellipse. So every point I really get an ellipse. So so what is really happening is that this is something like this and the intersection here is an ellipse for every point it is an ellipse. Yeah. Yeah. Yeah. Mhm. Mhm. Yeah. Yeah. Mhm.