Give a geometric description of the set of points in space whose coordinates sat

Question

Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations.
ive a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. Choose the correct answer below O A. The solid upper hemisphere cut from the sphere x+y +22-4 by the xz-plane (the plane y 0); the hemisphere has O B. The circle x +22 -4 in the xz-plane O C The cirole x +22 -4. y-0, together with its interior radius 2 and is centered at (0,0,0) D. The hollow upper hemisphere cut from the sphere x +y 22 4 by the xz-plane (the plane y- 0 ); the hemisphere has radius 2 and is centered at (0.0.0)

Explanation / Answer

x2 + y2 + z2 = 4 is a sphere centerred at origin and radius = 2;
However, when y=0, this equation reduces to x2 + z2 = 4
This, is the equation of a circle, centerend at (0,0,0) and has the radius =2;

Thus, the correct answer is option B: The circle x2 + z2 = 4 in the xz plane;

Note: since the sign is of equality and not inequality, it will not include the interiors.
For interiors to be included, the sign should be <= 4 and not =4;

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