Question

On a coordinate plane, a circle has a center at (negative 2, 1). Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0

Answer 1

Options A and B are correct.

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.

Answer 2

The answer is: the first and the second are correct

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