Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } + 18 x - 4 y + 76 = 0$$
A) center: (-2, 9); radius: 9
B) center: (9, -2); radius: 9
C) center: (2, -9); radius: 3
D) center: (-9, 2); radius: 3

Question

Quizplus · Accepted Answer

To find the center and radius of the circle given by the equation $x^2 + y^2 + 18x - 4y + 76 = 0$, we complete the square for both $x$ and $y$. The general form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius.Rearrange the equation: $x^2 + 18x + y^2 - 4y = -76$.Complete the square for $x$ and $y$:- For $x^2 + 18x$, add and subtract $(\frac{18}{2})^2 = 81$, resulting in $x^2 + 18x + 81$.- For $y^2 - 4y$, add and subtract $(\frac{4}{2})^2 = 4$, resulting in $y^2 - 4y + 4$.The equation becomes $x^2 + 18x + 81 + y^2 - 4y + 4 = -76 + 81 + 4$, which simplifies to $(x + 9)^2 + (y - 2)^2 = 9$.Thus, the center is $(-9, 2)$ and the radius is $\sqrt{9} = 3$.

Find the Center and Radius of the Circle x2+y2+18x−4y+76=0x ^ { 2 } + y ^ { 2 } + 18 x - 4 y + 76 = 0x2+y2+18x−4y+76=0

Find the Center and Radius of the Circle $x ^ { 2 } + y ^ { 2 } + 18 x - 4 y + 76 = 0$