How many distinct spheres of radius r can be | vedclass

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(D) sphere touching all three coordinate planes ($xy$,$yz$,and $zx$) must have its center at a point $(\pm r, \pm r, \pm r)$.Since there are $3$ coord

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$8$

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(D) sphere touching all three coordinate planes ($xy$,$yz$,and $zx$) must have its center at a point $(\pm r, \pm r, \pm r)$.Since there are $3$ coordinate planes and the sphere must be tangent to all of them,the distance from the center to each plane must be equal to the radius $r$.There are $2^3 = 8$ possible combinations of signs for the coordinates of the center $(\pm r, \pm r, \pm r)$.Thus,there are $8$ distinct spheres of radius $r$ that touch all three coordinate planes,one in each octant of the $3D$ coordinate system.

How many distinct spheres of radius $r$ can be drawn such that they touch all three coordinate planes?

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