Math Problem Statement
Find equations of two spheres that are centered at the origin and are tangent to the sphere of radius r = 1 centered at (3, −2, 4).
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
3D Coordinate Geometry
Spheres
Tangency
Formulas
Equation of a sphere: (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = r^2
Distance between two points in 3D: d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Theorems
Tangency condition between two spheres
Distance formula in 3D
Suitable Grade Level
Grades 11-12 or College
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