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In the 
xy-plane, Circle 
A is represented by the equation 
(x-2)^(2)+(y+3)^(2)=1, and Circle 
B is represented by the equation 
(x+2)^(2)+(y+5)^(2)=1. Which of the following statements about the two circles is true?
Choose 1 answer:
(A) Circle 
B is 2 units to the left of and 2 units below Circle 
A.
(B) Circle 
B is 2 units to the right of and 2 units above Circle 
A.
(C) Circle 
B is 4 units to the left of and 2 units below Circle 
A.
(D) Circle 
B is 4 units to the right of and 2 units above Circle 
A.

In the xy x y -plane, Circle A A is represented by the equation (x2)2+(y+3)2=1 (x-2)^{2}+(y+3)^{2}=1 , and Circle B B is represented by the equation (x+2)2+(y+5)2=1 (x+2)^{2}+(y+5)^{2}=1 . Which of the following statements about the two circles is true?\newlineChoose 11 answer:\newline(A) Circle B B is 22 units to the left of and 22 units below Circle A A .\newline(B) Circle B B is 22 units to the right of and 22 units above Circle A A .\newline(C) Circle B B is 44 units to the left of and 22 units below Circle A A 00.\newline(D) Circle B B is 44 units to the right of and 22 units above Circle A A .

Full solution

Q. In the xy x y -plane, Circle A A is represented by the equation (x2)2+(y+3)2=1 (x-2)^{2}+(y+3)^{2}=1 , and Circle B B is represented by the equation (x+2)2+(y+5)2=1 (x+2)^{2}+(y+5)^{2}=1 . Which of the following statements about the two circles is true?\newlineChoose 11 answer:\newline(A) Circle B B is 22 units to the left of and 22 units below Circle A A .\newline(B) Circle B B is 22 units to the right of and 22 units above Circle A A .\newline(C) Circle B B is 44 units to the left of and 22 units below Circle A A 00.\newline(D) Circle B B is 44 units to the right of and 22 units above Circle A A .
  1. Identify Centers: Identify the centers of Circle A and Circle B by examining their equations.\newlineCircle A: (x2)2+(y+3)2=1(x-2)^2 + (y+3)^2 = 1\newlineCircle B: (x+2)2+(y+5)2=1(x+2)^2 + (y+5)^2 = 1\newlineThe center of Circle A is at (2,3)(2, -3) and the center of Circle B is at (2,5)(-2, -5).
  2. Compare X-coordinates: Compare the xx-coordinates of the centers of Circle A and Circle B to determine their horizontal relative positions.\newlineThe xx-coordinate of Circle A's center is 22, and the xx-coordinate of Circle B's center is 2-2.\newlineCircle B is 2(2)=42 - (-2) = 4 units to the left of Circle A.
  3. Compare Y-coordinates: Compare the yy-coordinates of the centers of Circle A and Circle B to determine their vertical relative positions.\newlineThe yy-coordinate of Circle A's center is 3-3, and the yy-coordinate of Circle B's center is 5-5.\newlineCircle B is 5(3)=2-5 - (-3) = 2 units below Circle A.
  4. Combine Relative Positions: Combine the horizontal and vertical relative positions to determine the correct statement about the positions of Circle A and Circle B.\newlineCircle B is 44 units to the left of and 22 units below Circle A.

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