Find an equation of the sphere that passes through the origin and whose center is (5, -8, -10). the equation equals 0

Urijah Estes 2022-07-25 Answered
Find an equation of the sphere that passes through the origin and whose center is (5, -8, -10). the equation equals 0
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Answers (2)

Julianna Bell
Answered 2022-07-26 Author has 19 answers
Equation to the sphere with centre ( x 1 , y 1 , z 1 ) and radius a
is ( x x 1 ) 2 + ( y y 1 ) 2 + ( z z 1 ) 2 = a 2
here ( x 1 , y 1 , z 1 ) = ( 5 , 8 , 10 )
i.e. ( x 5 ) 2 + ( y + 8 ) 2 + ( z + 10 ) 2 = a 2
and this sphere is passes through the origin so
( 0 5 ) 2 + ( 0 + 8 ) 2 + ( 0 + 10 ) 2 = a 2
a 2 = 189
Now required sphere equation is
( x 5 ) 2 + ( y + 8 ) 2 + ( z + 10 ) 2 = 189
x 2 + y 2 + z 2 + 189 189 10 x + 16 y + 20 z = 0
x 2 + y 2 + z 2 10 x + 16 y + 20 z = 0

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pliwraih
Answered 2022-07-27 Author has 4 answers
the equation of sphere that passes through the origin can be written as
x 2 + y 2 + z 2 = R 2 (R is the radius)
since it pass (5, -8, -10)., we have:
5 2 + ( 8 ) 2 + ( 10 ) 2 = R 2
R 2 = 189
the equation of sphere is
x 2 + y 2 + z 2 = 189
R = 189 is the radius

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