Find an equation of the sphere that passes through the origin and whose center is (9, 9, 1).

sarahkobearab4

sarahkobearab4

Answered question

2022-08-04

Find an equation of the sphere that passes through the origin and whose center is (9, 9, 1).

Answer & Explanation

raffatoaq

raffatoaq

Beginner2022-08-05Added 22 answers

the sphere center (9,9,1) is
( x 9 ) 2 + ( y 9 ) 2 + ( z 1 ) 2 = R 2 R is the radius
since it passes (0,0,0)
we have:
( 0 9 ) 2 + ( 0 9 ) 2 = ( 0 1 ) 2 = R 2
R 2 = 81 + 81 + 1 = 163
( x 9 ) 2 + ( y 9 ) 2 + ( z 1 ) 2 = 163
the radius is R = 163
Marco Hudson

Marco Hudson

Beginner2022-08-06Added 5 answers

Since the origin is a point on the sphere, then the radius is the distance from the center to the origin.
r = 9 2 + 9 2 + 1 2 = 163
therefore the equation of the sphere is.
( x 9 ) 2 + ( y 9 ) 2 + ( z 1 ) 2 = 163

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