Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$$

A) $( x + 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$
Center: $( 4 , - 5 ) ; r = 4$

B) $( x + 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$
Center: $( - 4,5 ) ; r = 4$

C) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
Center: $( 8 , - 10 ) ; r = 25$

D) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
Center: $( - 8,10 ) ; r = 25$

Question

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$$

A) $( x + 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$
Center: $( 4 , - 5 ) ; r = 4$

B) $( x + 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$
Center: $( - 4,5 ) ; r = 4$

C) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
Center: $( 8 , - 10 ) ; r = 25$

D) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
Center: $( - 8,10 ) ; r = 25$

Quizplus · Accepted Answer

To rewrite 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 $x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$. Group $x$ and $y$ terms: $(x^2 + 8x) + (y^2 - 10y) = -25$. To complete the square, add and subtract $(\frac{8}{2})^2 = 16$ for $x$ and add and subtract $(\frac{10}{2})^2 = 25$ for $y$, then rearrange: $(x^2 + 8x + 16) + (y^2 - 10y + 25) = -25 + 16 + 25$. This simplifies to $(x + 4)^2 + (y - 5)^2 = 16$, which matches choice B. The center is at $(-4, 5)$ and the radius $r = \sqrt{16} = 4$.

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 $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$