Find the center of each circle. Match each of the equations with coordinates ( x , y ) to obtain a true statement.
-$( 8,10 )$
A) $x ^ { 2 } + y ^ { 2 } - 16 x - 20 y - 992 = 0$
B) $x ^ { 2 } + y ^ { 2 } + 18 x - 16 y + 144 = 0$
C) $x ^ { 2 } + y ^ { 2 } + 20 x + 16 y + 163 = 0$
D) $x ^ { 2 } + y ^ { 2 } - 8 x + 6 y + 9 = 0$

Question

Find the center of each circle. Match each of the equations with coordinates ( x , y ) to obtain a true statement.
-$( 8,10 )$ 
A) $x ^ { 2 } + y ^ { 2 } - 16 x - 20 y - 992 = 0$ 
B) $x ^ { 2 } + y ^ { 2 } + 18 x - 16 y + 144 = 0$ 
C) $x ^ { 2 } + y ^ { 2 } + 20 x + 16 y + 163 = 0$ 
D) $x ^ { 2 } + y ^ { 2 } - 8 x + 6 y + 9 = 0$

Quizplus · Accepted Answer

The center of a circle given by the equation $x^2 + y^2 + Dx + Ey + F = 0$ is $(-D/2, -E/2)$. For choice A, $D = -16$ and $E = -20$, so the center is $(16/2, 20/2) = (8, 10)$, matching the given coordinates.

Find the Center of Each Circle (8,10)( 8,10 )(8,10) A) x2+y2−16x−20y−992=0x ^ { 2 } + y ^ { 2 } - 16 x - 20 y - 992 = 0x2+y2−16x−20y−992=0

Find the Center of Each Circle $( 8,10 )$ A) $x ^ { 2 } + y ^ { 2 } - 16 x - 20 y - 992 = 0$