How do you find an equation of the sphere that passes through the point (9, 4,-6) and has a center (6,7,2)?

1 Answer
Alan P.
Feb 19, 2015

Find the equation for the equivalent sphere centered at (0,0,0) and then shift the co-ordinates.

(9,4,-6) relative to a center (6,7,2)
is equivalent to (3,-3,-8) relative to (0,0,0)

The equation of a sphere through (3,-3,-8) with center (0,0,0) is

X^2 + Y^2 + Z^2 = (3)^2 + (-3)^2 + (-8)^2
or
X^2 + Y^2 + Z^2 = 82

For (x,y,z) = (6,7,2) to be equivalent to (X,Y,Z) = (0,0,0)
X = x-6
Y = y-7
Z = z-2

So the desired equations is:
(x-6)^2 + (y-7)^2 + (z-2)^2 = 82

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