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Describe the given surface z = sqrt(1-(x^2+y^2)) a. cone b. top half of sphere c. top...

Describe the given surface

z = sqrt(1-(x^2+y^2))

a. cone b. top half of sphere c. top half of ellipsoid d. paraboloid

Math   Advanced-Math   
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Homework Answers

Answer #1

The graph of the given equation in 3D is given by

Z=(1-(X^2+Y^2))^1/2.Now taking square both side we get a equation Z^2+X^2+Y^2=1

SPHERE AND ElLIPSOIDS:

A sphere is graph of a equation of the form x^2+y^2+z^2=p^2 for some real number p.The radius of sphere is p.Ellipsoids are the graph of equation of the form a(x^2)+b(y^2)+c(z^2)=p^2 where a,b,c are all positive .In particular ,a sphere is a very special ellipsoid for which a,b and c are equal.

so second option is correct

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