Find radius and center of each sphere. x^2 +y^2 +z^2 +2x-2z=-1

Loldi9s

Loldi9s

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2022-09-03

Find radius and center of each sphere.
x 2 + y 2 + z 2 + 2 x 2 z = 1

Answer & Explanation

Trevon Hughes

Trevon Hughes

Beginner2022-09-04Added 9 answers

x 2 + y 2 + z 2 + 2 x 2 = 1, now groups together and then completed square
( x 2 + 2 x ) + y 2 + ( z 2 2 z ) = 1, each one you comleted ( b / 2 ) 2 add both side same value
( x 2 + 2 x + 1 ) + y 2 + ( z 2 2 z + 1 ) = 1 + 1 + 1
( x + 1 ) 2 + y 2 + ( z 1 ) 2 = 1
center: (-1,0,1),r=1
alan3885uo

alan3885uo

Beginner2022-09-05Added 3 answers

x 2 + y 2 + z 2 + 2 x 2 z = 1
x 2 + 2 x + y 2 + z 2 2 z = 1
( x 2 + 2 x + 1 ) + y 2 + ( z 2 2 z + 1 ) = 1 + 1 + 1 You want to complete the square to get the equation into the right form.
( x + 1 ) 2 + y 2 + ( z 1 ) 2 = 1
center: ( -1, 0, 1)
radius: 1 = 1

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