Find the center and radius of the circle by completing the square.
-$x^{2}-4 x+y^{2}-6 y+1=0$
A) $(-2,-3) ; r=12$
B) $(-2,-3) ; r=2 \sqrt{3}$
C) $(2,3) ; r=12$
D) $(2,3) ; r=2 \sqrt{3}$

Question

Quizplus · Accepted Answer

To find the center and radius, complete the square for both x and y terms:  $x^2 - 4x$ becomes $(x-2)^2 - 4$ and $y^2 - 6y$ becomes $(y-3)^2 - 9$.  The equation becomes $(x-2)^2 + (y-3)^2 = 12$.  Thus, the center is $(2,3)$ and the radius is $\sqrt{12} = 2\sqrt{3}$.

Find the Center and Radius of the Circle by Completing x2−4x+y2−6y+1=0x^{2}-4 x+y^{2}-6 y+1=0x2−4x+y2−6y+1=0

Find the Center and Radius of the Circle by Completing $x^{2}-4 x+y^{2}-6 y+1=0$