Describe in words the region of R^{3} represented by the equation(s) or inequality. x^{2} + y^{2} = 4

Nannie Mack 2020-12-29 Answered
Describe in words the region of R3 represented by the equation(s) or inequality.
x2+y2=4
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tafzijdeq
Answered 2020-12-30 Author has 92 answers

Concept:
The equation x2+y2=r2 represents a circle whose centre lies on z - axis
Given:
x2+y2=4
3) Calculation:
The given equation is
x2+y2=4
The equation x2+y2=4
represents the set of all points in R3 lying on circle x2+y2=4.
That is,
(x,y,z)|x2+y2=4,xR,yR,zR
Here is no restriction on z-coordinate, so a point in the region must lie on a circle with radius 2 and centre on z-axis but it could be any horizontal plane z=k (parallel to xy - plane)
Therefore, the region consists of all points on the circle x2+y2=4,z=k
That is, a circular cylinder with radius 2 whose axis is the z - axis
Therefore, the given equations represents the region in R3 consisting of all possible citcles of radius 2 and centre on z -axis that 1s a circular cylinder with radius 2 whose axis is the z - axis.
Conclusion:
The given equations represents the region in R3 consisting of all possible circles of radius 2 and centre on z - axis that is a circular cylinder with radius 2 whose axis is the z - axis.

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