Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$$
A) $( x + 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

B) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( - 3,3 ) ; r = 10$

C) $( x + 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

D) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

Question

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$$
A) $( x + 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

B) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( - 3,3 ) ; r = 10$

C) $( x + 3 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

D) $( x - 3 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 100$
Center: $( 3 , - 3 ) ; r = 10$

Quizplus · Accepted Answer

To rewrite the equation in the form $(x - h)^2 + (y - k)^2 = r^2$, we complete the square for both $x$ and $y$. The given equation is $x^2 + y^2 - 6x + 6y - 82 = 0$. For $x$, we add and subtract $(\frac{6}{2})^2 = 9$, and for $y$, we add and subtract $(\frac{6}{2})^2 = 9$, resulting in $x^2 - 6x + 9 + y^2 + 6y + 9 = 82 + 9 + 9$, which simplifies to $(x - 3)^2 + (y + 3)^2 = 100$. The center is $(3, -3)$ and the radius $r = \sqrt{100} = 10$.

Write the Given Equation in the Form (x−h)2+(y−k)2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h)2+(y−k)2=r2

Write the Given Equation in the Form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$