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.
Q. 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.
Circle A Equation: Circle A is represented by the equation (x−2)2+(y+3)2=1. The center of Circle A is at the point (2,−3).
Circle B Equation: Circle B is represented by the equation (x+2)2+(y+5)2=1. The center of Circle B is at the point (−2,−5).
Comparison of Centers: To compare the positions of Circle A and Circle B, we need to look at the differences in the x-coordinates and y-coordinates of their centers.
Difference in X-coordinates: The difference in the x-coordinates of the centers of Circle A and Circle B is −2−2=−4. This means Circle B is 4 units to the left of Circle A.
Difference in Y-coordinates: The difference in the y-coordinates of the centers of Circle A and Circle B is −5−(−3)=−2. This means Circle B is 2 units below Circle A.
Position Comparison: Based on the differences in the coordinates of the centers, the correct statement about the positions of Circle A and Circle B is that Circle B is 4 units to the left of and 2 units below Circle A.
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