Question 1034727
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Give a geometric description of the following problem:
{{{ x^2 + y^2 + z^2 = 4 }}}, {{{ y = x }}}

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I know that it is some kind of a sphere. But the {{{ y = x }}} part is throwing me off.

Thank you!
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First equation describes the sphere in 3D of the radius 2 with the center at the origin of the coordinate system.


The second equation describes the plane in the same 3D space. It passes through the origin of the coordinate system and contains the axis z.


Together, they describe the section of the sphere by the plane (their common points), which is a circle. It is a diametric section of the sphere.