Complete the square and write the equation in standard form. Then give the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } - 12 x - 10 y = - 12$$
A) $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 49$
$( 6,5 ) , r = 7$
B) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 49$
$( 5,6 ) , r = 7$
C) $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 49$
$( - 6 , - 5 ) , r = 49$
D) $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 49$
$( - 5 , - 6 ) , r = 49$

Question

Quizplus · Accepted Answer

To complete the square, group the x and y terms: $x^2 - 12x + y^2 - 10y = -12$. For x, add and subtract $(\frac{12}{2})^2 = 36$, and for y, add and subtract $(\frac{10}{2})^2 = 25$, resulting in $x^2 - 12x + 36 + y^2 - 10y + 25 = -12 + 36 + 25$. This simplifies to $(x - 6)^2 + (y - 5)^2 = 49$, which matches choice A. The center is at (6, 5) and the radius is $\sqrt{49} = 7$.

Complete the Square and Write the Equation in Standard Form x2+y2−12x−10y=−12x ^ { 2 } + y ^ { 2 } - 12 x - 10 y = - 12x2+y2−12x−10y=−12

Complete the Square and Write the Equation in Standard Form $x ^ { 2 } + y ^ { 2 } - 12 x - 10 y = - 12$