Identify the center and radius of the circle.
-$$x ^ { 2 } - 10 x + y ^ { 2 } = 11$$
A) Center: $( 10,0 ) ; \quad r = 36$
B) Center: $( 0 , - 5 ) ; \quad r = 6$
C) Center: $( 5,0 ) ; \quad r = 6$
D) Center: $( 10,0 ) ; \quad r = \sqrt { 11 }$

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 - 10x + y^2 = 11$, we complete the square for the x-terms. The equation can be rewritten as $(x^2 - 10x + 25) + y^2 = 11 + 25$ to complete the square, resulting in $(x - 5)^2 + y^2 = 36$. This shows the circle has a center at $(5, 0)$ and a radius $r = \sqrt{36} = 6$.

Identify the Center and Radius of the Circle x2−10x+y2=11x ^ { 2 } - 10 x + y ^ { 2 } = 11x2−10x+y2=11

Identify the Center and Radius of the Circle $x ^ { 2 } - 10 x + y ^ { 2 } = 11$