Find the center of the sphere whose equation is $x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } = 0$ .
A)(2, 1, 0)
B) $( 2 , - 1,0 )$
C) $( - 2,1,0 )$
D) $( - 2 , - 1,0 )$
E) $\left( 1 , \frac { 1 } { 2 } , 0 \right)$
F) $\left( - 1 , \frac { 1 } { 2 } , 0 \right)$
G) $\left( 1 , - \frac { 1 } { 2 } , 0 \right)$
H) $\left( - 1 , - \frac { 1 } { 2 } , 0 \right)$

Question

Find the center of the sphere whose equation is $x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } = 0$ .
A)(2, 1, 0)
B) $( 2 , - 1,0 )$ 
C) $( - 2,1,0 )$ 
D) $( - 2 , - 1,0 )$ 
E) $\left( 1 , \frac { 1 } { 2 } , 0 \right)$ 
F) $\left( - 1 , \frac { 1 } { 2 } , 0 \right)$ 
G) $\left( 1 , - \frac { 1 } { 2 } , 0 \right)$ 
H) $\left( - 1 , - \frac { 1 } { 2 } , 0 \right)$

Quizplus · Accepted Answer

The equation of the sphere can be rewritten by completing the square: $(x+1)^2 - 1 + (y-\frac{1}{2})^2 - \frac{1}{4} + z^2 = 0$. The center is $(-1, \frac{1}{2}, 0)$.

Find the Center of the Sphere Whose Equation Is x2+2x+y2−y+z2=0x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } = 0x2+2x+y2−y+z2=0

Find the Center of the Sphere Whose Equation Is $x ^ { 2 } + 2 x + y ^ { 2 } - y + z ^ { 2 } = 0$