Respuesta :
Answer:
The answer is: the first and the second are correct
Step-by-step explanation:
Data:
Center: (-2, 1)
a) x2 + y2 + 4x – 2y – 4 = 0
x2 + 4x +y2 - 2y = 4
(x+2)2 + (y-1)2 = 4+4+1 = 9 Center = (-2,1) Correct
b) x2 + y2 + 4x – 2y + 2 = 0
(x + 2)2 + (y-1)2 = -2+4+1 = 3 Center = (-2,1) Correct
c) x2 + y² – 4x + 2y – 4 = 0
(x-2)2 + (y-1) = 4 + 4 +1 = 9 Center = (2,1) Incorrect
d) x2 + y² – 4x + 2y + 2 = 0
(x-2)2 + (y -1)2 = -2+4+1 = 3 Center = (2,1) Incorrect
Answer:
Options A and B are correct.
Step-by-step explanation:
To get the correct answer we will convert each equation in the center radius form.
A). x² + y² + 4x - 2y - 4 = 0
x² + y² + 4x - 2y = 4
x² + 4x + 4 - 4 + y² - 2y + 1 - 1 = 4
(x + 2)²+ (y - 1)² - 5 = 4
(x + 2)²+ (y - 1)²= 9
Therefore, center of the circle is (-2, 1).
B). x² + y² + 4x - 2y + 2 = 0
x² + y² + 4x - 2y = -2
x² + 4x + 4 - 4 + y² - 2y + 1 - 1 = -2
(x + 2)² + (y - 1)² -5 = -2
(x + 2)² + (y - 1)²= -2+ 5
(x + 2)² + (y - 1)² = 3
Center of this circle is (-2, 1)
C). x² + y² - 4x + 2y - 4 = 0
(x² - 4x + 4 - 4) + (y² + 2y + 1 - 1) = 4
[(x - 2)² - 4]+ [(y + 1)²- 1] = 4
(x -2)² + (y + 1)² = 9
Center of this circle is (2, -1).
D). x² + y² - 4x + 2y + 2 = 0
x² - 4x + 4 - 4 + y² + 2y + 1 - 1 = -2
(x - 2)² - 4 + (y + 1)² - 1 = -2
(x -2)² + (y + 1)² - 5 = -2
(x -2)² + (y + 1)² = 3
Center of this circle is (2, -1)
Options A and B are correct.
