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.
Analyze Circle A: Analyze the equation of Circle A.The equation of Circle A is given by (x−2)2+(y+3)2=1. This equation represents a circle with a center at (2,−3) and a radius of 1 (since the radius squared is 1).
Analyze Circle B: Analyze the equation of Circle B.The equation of Circle B is given by (x+2)2+(y+5)2=1. This equation represents a circle with a center at (−2,−5) and a radius of 1 (since the radius squared is 1).
Compare Centers: Compare the centers of Circle A and Circle B. Circle A has a center at (2,−3) and Circle B has a center at (−2,−5). To find the relative position of Circle B with respect to Circle A, we need to compare their x-coordinates and y-coordinates.
Calculate Differences: Calculate the difference in x-coordinates and y-coordinates.The difference in x-coordinates is −2−2=−4, which means Circle B is 4 units to the left of Circle A.The difference in y-coordinates is −5−(−3)=−2, which means Circle B is 2 units below Circle A.
Determine Correct Statement: Determine the correct statement.Based on the calculations, Circle B is 4 units to the left of and 2 units below Circle A. This corresponds to option (C).
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