Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } - 2 x + 10 y - 55 = 0$$
A) center: $( - 5,1 )$; radius: 9
B) center: $( 5 , - 1 )$; radius: 81
C) center: $( - 1,5 )$; radius: 81
D) center: $( 1 , - 5 )$; radius: 9

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 + y^2 - 2x + 10y - 55 = 0$, we complete the square for both $x$ and $y$. Completing the square for $x^2 - 2x$ gives $(x-1)^2 - 1$, and for $y^2 + 10y$ gives $(y+5)^2 - 25$. Adding these adjustments to both sides, the equation becomes $(x-1)^2 + (y+5)^2 = 81$. Thus, the center is $(1, -5)$ and the radius is $\sqrt{81} = 9$.

Find the Center and Radius of the Circle x2+y2−2x+10y−55=0x ^ { 2 } + y ^ { 2 } - 2 x + 10 y - 55 = 0x2+y2−2x+10y−55=0

Find the Center and Radius of the Circle $x ^ { 2 } + y ^ { 2 } - 2 x + 10 y - 55 = 0$