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Use traces to sketch and identify the surface.

$ z^2 - 4x^2 - y^2 = 4 $

hyperboloid of two sheets

Vectors

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Missouri State University

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University of Nottingham

in the problem. And we have given an equation that is did Squire minus four X Squire minus y square. That is equal to four. So here is that it's quite equal. Four plus four X Squire minus Y. Sorry this is plus Y square. So J equals route over off four mine plus four x square plus y squared. Now here we will put the value of X and y zero. Therefore zero is equal to No tomorrow. For that is equal to plus -2. Now The value of Jade equals plus -2. This is the real value of debt. Now here we have X equal so minus four X squared is equal to four minus jet square plus y squared. So here it is four get square and plus weisglass. Now ex Squire becomes minus one and it is Plus Jade Square upon four. My nurse, why square upon for our eggs becomes route ovtcharov minus one plus j disk wired upon food minus y squared upon before. Now when we put the value of a J D n Y zero. Therefore this equation becomes so X equals plus minus over time. So it's a complex number now. For value of why we have Y squared equal food Or rather it is -4 minus jade Squire Plus four x squared. So why is equal the route over half minus four minus that Squire plus four X square. So here kill those mistakes here. So we have Y equals plus minus two area. So this is also a complex number X and Y is complex number. But jade is a real number. Therefore the center of the curve lies on jet equals plus minus two. So this is the point, that is, this is the mm point. This is too, And this is also -2. We have ex excess Y axis and jx so J equals plus minus two is the value, and X and y are the complex numbers. So we have The value of debt equals -2. Sorry, there's a blast to hear and -2 here. So this is the car for this equation and this is the answer to the problem.