Find the center of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 6 x + 4 y + 9 = 0$
A)Center: $( 3 , - 2,0 )$
B)Center: $( - 3 , - 2,0 )$
C)Center: $( - 3,2,0 )$
D)Center: $( 0 , - 2,0 )$
E)Center: $( 3,0,0 )$

Question

Find the center of the sphere.  $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 6 x + 4 y + 9 = 0$ 
A)Center: $( 3 , - 2,0 )$
B)Center: $( - 3 , - 2,0 )$
C)Center: $( - 3,2,0 )$
D)Center: $( 0 , - 2,0 )$
E)Center: $( 3,0,0 )$

Quizplus · Accepted Answer

To find the center of the sphere given by the equation $x^2 + y^2 + z^2 - 6x + 4y + 9 = 0$, we complete the square for $x$, $y$, and $z$. The equation can be rewritten as $(x-3)^2 + (y+2)^2 + z^2 = 9$, indicating the center is at $(3, -2, 0)$.

Find the Center of the Sphere x2+y2+z2−6x+4y+9=0x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 6 x + 4 y + 9 = 0x2+y2+z2−6x+4y+9=0

Find the Center of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 6 x + 4 y + 9 = 0$