Find the center and the radius of the circle.
-$x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0$
A) center $( 5 , - 1 )$, radius $= 2 \sqrt { 2 }$
B) center $( 5 , - 1 )$, radius $= 8$
C) center $( - 5,1 )$, radius $= 8$
D) center $( - 5,1 )$, radius $= 2 \sqrt { 2 }$

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 + y^2 + 10x - 2y + 18 = 0$, we complete the square for both $x$ and $y$. Completing the square for $x^2 + 10x$ gives $(x+5)^2 - 25$, and for $y^2 - 2y$ gives $(y-1)^2 - 1$. Substituting these into the original equation and simplifying gives $(x+5)^2 + (y-1)^2 = 8$, which shows the center is $(-5, 1)$ and the radius is $\sqrt{8} = 2\sqrt{2}$.

Find the Center and the Radius of the Circle x2+y2+10x−2y+18=0x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0x2+y2+10x−2y+18=0

Find the Center and the Radius of the Circle $x ^ { 2 } + y ^ { 2 } + 10 x - 2 y + 18 = 0$