Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$$
A) $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( - 22,0 ) ; r = 21$

B) $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( 0,22 ) ; r = 21$

C) $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( - 11,0 ) ; r = 10$

D) $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( 0,11 ) ; r = 10$

Question

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius.
-$$x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$$
A) $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( - 22,0 ) ; r = 21$

B) $( x + 22 ) ^ { 2 } + y ^ { 2 } = 21$
Center: $( 0,22 ) ; r = 21$

C) $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( - 11,0 ) ; r = 10$

D) $( x + 11 ) ^ { 2 } + y ^ { 2 } = 100$
Center: $( 0,11 ) ; r = 10$

Quizplus · Accepted Answer

To write the equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$, complete the square for the x-terms. The given equation is $x ^ { 2 } + y ^ { 2 } + 22 x + 21 = 0$. Completing the square for the x-term involves adding and subtracting $(\frac{22}{2})^2 = 121$, leading to $x ^ { 2 } + 22 x + 121 + y ^ { 2 } = -21 + 121$, which simplifies to $(x + 11)^2 + y^2 = 100$. The center is $(-11, 0)$ 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 $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$