Find the center and radius of the circle.
-$x ^ { 2 } + y ^ { 2 } + 18 x + 4 y + 85 = 36$
A) $( 9,2 ) , r = 36$
B) $( - 9 , - 2 ) , \mathrm { r } = 6$
C) $( 2,9 ) , r = 36$
D) $( - 2 , - 9 ) , r = 6$

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 + y^2 + 18x + 4y + 85 = 36$, we complete the square for both $x$ and $y$. The equation can be rewritten as $x^2 + 18x + y^2 + 4y = -49$. Completing the square for $x$ and $y$ separately, we add and subtract $(18/2)^2 = 81$ for $x$ and add and subtract $(4/2)^2 = 4$ for $y$, leading to $x^2 + 18x + 81 + y^2 + 4y + 4 = -49 + 81 + 4$. This simplifies to $(x + 9)^2 + (y + 2)^2 = 36$, indicating a circle with center $(-9, -2)$ and radius $r = \sqrt{36} = 6$.

Find the Center and Radius of the Circle x2+y2+18x+4y+85=36x ^ { 2 } + y ^ { 2 } + 18 x + 4 y + 85 = 36x2+y2+18x+4y+85=36

Find the Center and Radius of the Circle $x ^ { 2 } + y ^ { 2 } + 18 x + 4 y + 85 = 36$