Rachel M.
asked • 01/09/24Clarification on equation of the sphere
Find the equation of the sphere of radius 6 that lies above the xy-plane that just touches the xy-plane at the point (3, −7, 0).
answer: (x-3)^2 + (y+7)^2 + (z-6)^2 = 6^2
It is on the xy-plane why do we add in the z part with the radius? Is it because z will eventually cancel out and become zero.
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1 Expert Answer
Yefim S. answered • 01/09/24
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Center of sphere is (3, - 7, 6) because (3, - 7, 0) is tangent point with xy plane and z = 6.
Because equation: (x - 3)2 + (y + 7)2 + (z - 6)2 = 36
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Doug C.
Ask yourself where is the center of the sphere? If it is tangent to the xy-plane at (3,-7,0), then a line through that point parallel to the z-axis will contain a diameter of the sphere. Since the radius is 6, up 6 along that line takes you to the point (3, -7,6)--the center of the sphere. Take a look here: desmos.com/3d/a8ba557f4601/09/24