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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 AA.\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 AA.\newline(D) Circle B B is 44 units to the right of and 22 units above Circle A A .
  1. Analyze Circle A: Analyze the equation of Circle A.\newlineThe equation of Circle A is given by (x2)2+(y+3)2=1(x-2)^2 + (y+3)^2 = 1. This equation represents a circle with a center at (2,3)(2, -3) and a radius of 11 (since the radius squared is 11).
  2. Analyze Circle B: Analyze the equation of Circle B.\newlineThe equation of Circle B is given by (x+2)2+(y+5)2=1(x+2)^2 + (y+5)^2 = 1. This equation represents a circle with a center at (2,5)(-2, -5) and a radius of 11 (since the radius squared is 11).
  3. Compare Centers: Compare the centers of Circle A and Circle B. Circle A has a center at (2,3)(2, -3) and Circle B has a center at (2,5)(-2, -5). To find the relative position of Circle B with respect to Circle A, we need to compare their xx-coordinates and yy-coordinates.
  4. Calculate Differences: Calculate the difference in xx-coordinates and yy-coordinates.\newlineThe difference in xx-coordinates is 22=4-2 - 2 = -4, which means Circle B is 44 units to the left of Circle A.\newlineThe difference in yy-coordinates is 5(3)=2-5 - (-3) = -2, which means Circle B is 22 units below Circle A.
  5. Determine Correct Statement: Determine the correct statement.\newlineBased on the calculations, Circle B is 44 units to the left of and 22 units below Circle A. This corresponds to option (C)(C).

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