Concept:
The equation \(x^{2} + y^{2} = r^{2}\) represents a circle whose centre lies on z - axis
Given:
\(x^{2} + y^{2} =4\)
3) Calculation:
The given equation is
\(x^{2} + y^{2} = 4\)
The equation \(x^{2} + y^{2} =4\)
represents the set of all points in \(R^{3}\ lying\ on\ circle\ x^{2} + y^{2} = 4.\)
That is,
\({(x, y, z) | x^{2} + y^{2} = 4, x \in R, y \in R, z \in R}\)
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 \(x^{2} + y^{2} = 4, z = k\)
That is, a circular cylinder with radius 2 whose axis is the z - axis
Therefore, the given equations represents the region in \(R^{3}\) 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 \(R^{3}\) 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.
Describe in words the region of R^{3} represented by the equation(s) or inequality. x^{2} + y^{2} = 4
Describe in words the region of R^{3} represented by the equation(s) or inequality. x^{2} + y^{2} = 4
Answers (1)
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