Find the equation of a sphere if one of its diameters has endpoints: (-8, -6, -17) and (12, 14, 3).

stratsticks57jl 2022-07-29 Answered
Find the equation of a sphere if one of its diameters has endpoints: (-8, -6, -17) and (12, 14, 3).
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Answers (2)

umgangistbf
Answered 2022-07-30 Author has 12 answers
The center of the sphere is the midpoint between the given points.
( ( 8 ) + ( 12 ) 2 , ( 6 ) + ( 14 ) 2 , ( 17 ) + ( 3 ) 2 ) = ( 2 , 4 , 7 )
the radius is the distance from the center to either point.
( 12 2 ) 2 + ( 14 4 ) 2 + ( 3 + 7 ) 2 = 300
since the equation of a sphere with center (H,K,L) and radius r is.
( x H ) 2 + ( y K ) 2 + ( z L ) 2 = r 2
then the equation is.
( x 2 ) 2 + ( y 4 ) 2 + ( z + 7 ) 2 + 300
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Alonzo Odom
Answered 2022-07-31 Author has 4 answers
The diameter length is
2 R = ( 8 12 ) 2 + ( 6 14 ) 2 + ( 17 3 ) 2 = 20 3
R = 10 3
the sphere equation is:
the center of the two points also the center of the sphere:
x c = 8 + 12 2 = 2 , y c = 6 + 14 2 = 4 , z c = 17 + 3 2 = 7
so the equation of the sphere is:
( x 2 ) 2 + ( y 4 ) 2 + ( z + 7 ) 2 = R 2 = 300
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