Find the center and radius of the circle.
-$x ^ { 2 } + y ^ { 2 } + 18 x + 2 y = - 46$
A) $( - 1 , - 9 ) , \mathrm { r } = 6$
B) $( 1,9 ) , r = 36$
C) $( 9,1 ) , r = 36$
D) $( - 9 , - 1 ) , \mathrm { r } = 6$

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 + y^2 + 18x + 2y = -46$, we complete the square for both $x$ and $y$. For $x$, we take the coefficient of $x$, which is 18, divide it by 2 to get 9, and square it to get 81. We add and subtract 81 inside the equation. For $y$, we take the coefficient of $y$, which is 2, divide it by 2 to get 1, and square it to get 1. We add and subtract 1 inside the equation. The equation becomes $x^2 + 18x + 81 + y^2 + 2y + 1 = -46 + 81 + 1$, which simplifies to $(x + 9)^2 + (y + 1)^2 = 36$. This shows the circle has a center at $(-9, -1)$ and a radius of $\sqrt{36} = 6$.

Find the Center and Radius of the Circle x2+y2+18x+2y=−46x ^ { 2 } + y ^ { 2 } + 18 x + 2 y = - 46x2+y2+18x+2y=−46

Find the Center and Radius of the Circle $x ^ { 2 } + y ^ { 2 } + 18 x + 2 y = - 46$