Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$$
A) $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( 16,8 ) ; r = 20$

B) $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( - 16 , - 8 ) ; r = 20$

C) $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( - 8 , - 4 ) ; r = 10$

D) $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( 8,4 ) ; r = 10$

Question

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 16 x + 8 y - 20 = 0$$
A) $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( 16,8 ) ; r = 20$

B) $( x + 16 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 20$
Center: $( - 16 , - 8 ) ; r = 20$

C) $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( - 8 , - 4 ) ; r = 10$

D) $( x + 8 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
Center: $( 8,4 ) ; r = 10$

Quizplus · Accepted Answer

To get the equation in the form $(x - h)^2 + (y - k)^2 = r^2$, complete the square for both $x$ and $y$. The given equation is $x^2 + y^2 + 16x + 8y - 20 = 0$. Completing the square:- For $x^2 + 16x$, add and subtract $(\frac{16}{2})^2 = 64$.- For $y^2 + 8y$, add and subtract $(\frac{8}{2})^2 = 16$.So, the equation becomes $x^2 + 16x + 64 + y^2 + 8y + 16 - 20 - 64 - 16 = 0$, which simplifies to $(x + 8)^2 + (y + 4)^2 = 100$. The center is at $(-8, -4)$ 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 $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$