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Numerade Educator

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Problem 46 Easy Difficulty

Find an equation for the surface obtained by rotating the line $ z = 2y $ about the z-axis.

Answer

$x^{2}+y^{2}=\frac{z^{2}}{4}$

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Video Transcript

in this problem, it is asked to find any question for the surface obtained by rotating the line that equals to two by about the by access. So, what does it mean? We have considered a book. Mhm. That is very equal to white. All right. So, now this curve is rotated about said access. That means this is nothing. But we need to replace. Why by That is why that is given to us. That is by route over its square place. Why is that? Right? So we need to do just one. So here this becomes very simple for the equation for the resulting surface will be what when we rotate about their access? Right? So this will this becomes is there any questions to root X squared plus Y. Is well, as we have already told that why will become at a square place twice favorite? Yeah. So, this will be given by This is four. We are just squaring it. Yes. So there's become four X squared plus Y square. And this side left inside becomes that square. So this becomes that's where is equal to four X squared plus poor race. But so this is the resulting equation for us. So this is how we solve this problem. I hope your industry, the concept. Thank you for watching.